RD SHARMA Solutions for Class 10 Maths Chapter 4 - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise 4.82

Question 1

If the equation x2 + 4x + k = 0 has real and distinct root, then

(a) k < 4

(b) k > 4

(c) k ≥ 4

(d) k ≤ 4

Solution 1

We know for the quadratic equation

ax2 + bx + c = 0

condition for roots to be real and distinct is

D = b2 - 4ac > 0       ..........(1)

for the given question

x+ 4x + k = 0

a = 1, b = 4, c = k

from (1)

16 - 4k > 0

k < 4

So, the correct option is (a).

Chapter 4 - Quadratic Equations Exercise 4.83

Question 1

The number of quadratic equations having real roots and which do not change by squaring their roots is

(a) 4

(b) 3

(c) 2

(d) 1

Solution 1

Any quadratic equation having roots 0 or 1 are only possible quadratic equation because on squaring 0 or 1, it remains same.

Hence, 2 solutions are possible, one having roots 1 and 1, while the other having roots 0 and 1.

So, the correct option is (c).

Question 2

If the equation x2 - ax + 1 = 0 has two distinct roots, then

(a) |a| = 2

(b) |a| < 2

(c) |a| > 2

(d) None of these

Solution 2

For the equation x2 - ax + 1 = 0 has two distinct roots, condition is

(-a)- 4 (1) (1) > 0

a- 4 > 0

a> 4

|a| > 2

So, the correct option is (c).

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

If the equation ax2 + 2x + a = 0 has two distinct roots, if

(a) a = ± 1

(b) a = 0

(c) a = 0, 1

(d) a = -1, 0

Solution 5

For any quadratic equation

ax + bx + c = 0

having two distinct roots, condition is

b2 - 4ac > 0

For the equation ax2 + 2x + a = 0 to have two distinct roots,

(2)2 - 4 (a) (a) > 0

4 - 4a2 > 0

4(1 - a2) > 0

1 - a2 > 0 since 4 > 0

that is, a2 - 1 < 0

Hence -1 < a < 1, only integral solution possible is a = 0

So, the correct option is (b).

Question 6

The positive value of k for which the equation x2 + kx + 64 = 0 and x2 - 8x + k = 0 will both have real roots, is

(a) 4

(b) 8

(c) 12

(d) 16

Solution 6

For any quadratic equation

ax2 + bx + c = 0

having real roots, condition is

b2 - 4ac ≥ 0     .......(1)

According to question 

x+ kx + 64 = 0 have real root if

k- 4 × 64 ≥ 0

k2 ≥ 256

|k|≥ 16             ........(2)

Also, x2 - 8x + k = 0 has real roots if

64 - 4k ≥ 0

k ≤ 16    .........(3)

from (2), (3) the only positive solution for k is

k = 16

So, the correct option is (d).

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

If 2 is a root of the equation x+ bx + 12 = 0 and the equation x2 + bx + q = 0 has equal roots, then q =

(a) 8

(b) -8

(c) 16

(d) -16

Solution 8

It is given that 2 is a root of equation x + bx + 12 = 0

Hence

(2)+ b(2) + 12 = 0

4 + 2b + 12 = 0

2b + 16 = 0

b = -8        .........(1)

It is also given that x2 + bx + q = 0 has equal root 

so, b2 - 4(q) = 0         ........(2)

from (1) & (2)

(-8)- 4q =0

q = 16

So, the correct option is (c).

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

For any quadratic equation

ax2 + bx + c = 0

Having equal roots, the condition is

b - 4ac = 0

For the equation

(a2 + b2) x2 - 2 (ac + bd)x + c2 + d= 0

to have equal roots, we have

(-2(ac + bd))- 4 (c+ d2) (a2 + b2) = 0

4 (ac + bd)- 4 (a2c+ b2c2 + d2a2 + b2d2) = 0

(a2c+ b2d2 + 2abcd) - (a2c+ b2c2 + a2d2+ b2d2) = 0

2abcd - b2c2 - a2d2 = 0

b2c2 - a2d- 2abcd = 0

(bc - ad)= 0

bc = ad

So, the correct option is (b).

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

For any quadratic equation

ax+ bx + c = 0

having equal roots, condition is

b2 - 4ac = 0

According to question, quadratic equation is

(a2 + b2)x2 - 2b(a + c)x + b2 + c= 0

having equal roots, so

(2b(a + c))2 - 4(a2 + b2) (b2 + c2) = 0

4b2 (a + c)2 - 4(a2b2 + a2c2 + b4 + b2c2) = 0

b2(a2 + c2 + 2ac) - (a2b2 + a2c+ b2c2 + b4) = 0

a2b2 + b2c2 + 2acb2 - a2b2 - a2c- b2c2 - b4 = 0

2acb2 - a2c2 - b4 = 0

a2c2 + b4 - 2acb2 = 0

(ac - b2)2 = 0

ac = b2

So, the correct option is (b).

Question 11

If the equation x2 - bx + 1 = 0 does not possess real roots, then

(a) -3 < b < 3

(b) -2 < b < 2

(c) b < 2

(d) b < -2

Solution 11

For any quadratic equation ax2 + bx + c = 0 having no real roots, condition is

b2 - 4ac < 0

For the equation, x2 - bx + 1 = 0 having no real roots

b2 - 4 < 0

b2 < 4

-2 < b < 2

So, the correct option is (b).

Question 12

If x = 1 is a common root of the equations ax2 + ax + 3 = 0 and x2 + x + b = 0, then ab =

(a) 3

(b) 3.5

(c) 6

(d) -3

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

If p and q are the roots of the equation x-px + q = 0, then

(a) p = 1, q = -2

(b) b = 0, q = 1

(c) p = -2, q = 0

(d) p = -2, q = 1

Solution 13

If p, q are the roots of equation x- px + q = 0, then p and q satisfies the equation

Hence

(p)- p(p) + q = 0

p- p+ q = 0

q = 0

and (q)- p(q) + q = 0

q- p(q) + q = 0

0 = 0

p can take any value

p = -2 and q = 0

So, the correct option is (c).

Question 14

If a and b can take values 1, 2, 3, 4. Then the number of the equations of the form ax2 + bx + 1 = 0 having real roots is

(a) 10

(b) 7

(c) 6

(d) 12

Solution 14

For the ax+ bx + 1 = 0 having real roots condition is

b- 4(a) (1) ≥ 0

b2 ≥ 4a

For a = 1

b2 ≥ 4

b ≥ 2

b can take value 2, 3, 4

Here, 3 possible solutions are possible            .......(1)

For a = 2

b2 ≥ 8

Here, b can take value 3, 4            ......(2)

Here, 2 solutions are possible

For a = 3

b≥ 12

possible value of b is 4

Hence, only 1 possible solution      ......(3)

For a = 4

b2 ≥ 16

possible value of b is 4

Hence, only 1 possible solution    .......(4)

from (1), (2), (3), (4)

Total possible solutions are 7

So, the correct option is (b).

Chapter 4 - Quadratic Equations Exercise 4.84

Question 1

If one root of the equation x2 + ax + 3 = 0 is 1, then its other root is

(a) 3

(b) -3

(c) 2

(d) -2

Solution 1

x+ ax + 3 = 0

product of roots = 3

One root is 1. Hence other root is 3.

So, the correct option is (a).

Question 2

If (a+ b2) x+ 2(ab + bd) x + c2 + d= 0 has no real roots, then

(a) ad = bc

(b) ab = cd

(c) ac = bd

(d) ad ≠ bc

Solution 2

If any quadratic equation ax+ bx + c has no real roots then b- 4ac < 0    ......(1)

According to the question, the equation is

(a+ b2) x+ 2(ac + bd) x + c2 + d= 0

from (1)

4(ac + bd)- 4(a2 + b2) (c2 + d2) < 0

a2c2 + b2d2 + 2abcd - (a2c2 + a2d2 + b2c2 + b2d2) < 0

a2c2 + b2d2 + 2abcd - a2c2 - a2d2 - b2c2 - b2d2 < 0

2abcd - a2d2 - b2c2 < 0

-(ad - bc)< 0

(ad - bc)> 0

For this condition to be true ad ≠ bc

So, the correct option is (d).

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

If x = 1 is a common root of ax+ ax + 2 = 0 and x+ x + b = 0 then, ab =

(a) 1

(b) 2

(c) 4

(d) 3

Solution 4

It is given that x = 1 is root of equation ax2 + ax + 2 = 0

Hence, a(1)2 + a(1) + 2 = 0

           2a + 2 = 0

           a = -1         ......(1)

It is given that x = 1 is also root of x2 + x + b = 0

Hence, (1)+ (1) + b = 0

           b = -2     ......(2)

from (1) & (2)

ab = (-1) (-2)

ab = 2

So, the correct option is (b).

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

If sin α and cos α are the roots of the equation ax+ bx + c = 0, then b2

(a) a- 2ac

(b) a+ 2ac

(c) a- ac

(d) a+ ac

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

If 2 is a root of the equation x+ ax + 12 = 0 and the quadratic equation x + ax + q = 0 has equal roots, then q =

(a) 12

(b) 8

(c) 20

(d) 16

Solution 9

Given, 2 is a root of equation x+ ax + 12 = 0

so (2)+ a(2) + 12 = 0

4 + 2a + 12 = 0

a = -8     .....(1)

Given x+ ax + q = 0 has equal roots so

a- 4q = 0   ......(2)

from (1) & (2)

(-8)- 4q = 0

4q = 64

q = 16

So, the correct option is (d).

Question 10

If the sum of the roots of the equation x2 - (k + 6)x + 2(2k - 1) = 0 is equal to half of their product, then k =

(a) 6

(b) 7

(c) 1

(d) 5

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

If a and b are roots of the equation x2 + ax + b = 0, then a + b =

(a) 1

(b) 2

(c) -2

(d) -1

Solution 11

If a and b are roots of the equation x+ ax + b = 0

Then, sum of roots = -a

a + b = -a

2a + b = 0          .......(1)

product of roots = b

ab = b

ab - b = 0

b(a - 1) = 0         ........(2)

from (1) and (2)

-2a(a - 1) = 0...(From (1), we have b = -2a)

a(a - 1) = 0

a = 0 or a = 1

if a = 0 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations b = 0

if a = 1 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations b = -2

Now a and b can't be zero at same time, so correct solution is

a = 1 and b = -2

a + b = -1

So, the correct option is (d).

Question 12

A quadratic equation whose one root is 2 and the sum of whose roots is zero, is

(a) x+ 4 = 0

(b) x- 4 = 0

(c) 4x- 1 = 0

(d) x- 2 = 0

Solution 12

Given sum of roots is zero and one root is 2.

So the other root must be -2

so any quadratic equation having root 2 and -2 is

(x - 2) (x - (-2)) = 0

(x - 2) (x + 2) = 0

x- 4 = 0

So, the correct option is (b).

Question 13

If one root of the equation ax+ bx + c = 0 is three times the other, then b2 : ac =

(a) 3 : 1

(b) 3 : 16

(c) 16 : 3

(d) 16 : 1

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

If one root of the equation 2x+ kx + 4 = 0 is 2, then the other root is

(a) 6

(b) -6

(c) -1

(d) 1

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise 4.85

Question 1

If one root of the equation 4x- 2x + (λ - 4) = 0 is a reciprocal of the other, then λ =

(a) 8

(b) -8

(c) 4

(d) -4

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Any quadratic equation, ax+ bx + c = 0 has real and equal roots if b- 4ac = 0

For the question, equation is 16x+ 4kx + 9 = 0,

(4k)- 4 × 16 × 9 = 0

16k- 36 × 16 = 0

k2 - 36 = 0

k= 36

k = ± 6

So, the correct option is (c).

Chapter 4 - Quadratic Equations Exercise Ex. 4.1

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

solutions of the equation 2x2 - x + 9 = x2 + 4x + 3 , x = 2 and x = 3

Solution 20

= 2x- x + 9 – x+ 4x + 3

= x2 - 5x + 6 = 0

Here, LHS = x2 - 5x + 6 and RHS = 0

Substituting x = 2 and x = 3

= x2 - 5x + 6

= (2)2 – 5(2) + 6

=10-10

=0

= RHS

= x2 - 5x + 6

= (3)2 – 5(3) + 6

= 9 - 15 + 6

=15 - 15

=0

= RHS

x = 2 and x = 3 both are the solutions of the given quadratic equation.

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.10

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

A pole has to be erected at a point on the boundary of a circular park of diameter 13 metres in such a way that the difference of its distances from two diametrically opposite fixed gates A and B on the boundary is 7 metres. Is it possible to do so? If yes, at what distances from the two gates should the pole be erected?

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.11

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Two squares have sides x cm and (x + 4) cm. The sum of their areas is 656 cm2. Find the sides of the squares.

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Is it possible to design a rectangular mango grove whose length is twice its breadth, and the area is 800 m2? If so, find its length and breadth.

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Sum of the areas of two squares is 640 m2. If the difference of their perimeter is 64 m, find the sides of the two squares.

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Sum of the areas of two squares is 400 cm2. If the difference of their perimeters is 16 cm, find the sides of two squares.

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

The area of a rectangular plot is 528 m2. The length of the plot (in meters) is one meter more than twice its breadth. Find the length and the breadth of the plot.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

In the centre of a rectangular lawn of dimension 50 m × 40 m, a rectangular pond has to be constructed so that the area of the grass surrounding the pond would be 1184 m2. Find the length and breadth of the pond.

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.12

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

To fill a swimming pool two pipes are used. If the pipe of larger diameter used for 4 hours and the pipe of smaller diameter for 9 hours, only half of the pool can be filled. Find, how long it would take for each pipe to fill the pool separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool?

Solution 5

Let us assume that the larger pipe takes 'x' hours to fill the pool.

So, as per the question, the smaller pipe takes 'x + 10' hours to fill the same pool.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Chapter 4 - Quadratic Equations Exercise Ex. 4.13

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations
Question 9

In a class test, the sum of the marks obtained by P in Mathematics and Science is 28. Had he got 3 marks more in Mathematics and 4 marks less in Science. The product of his marks, would have been 180. Find his marks in the two subjects.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was 3 more than twice the number of articles produced on that day. If the total cost of production on that day was Rs 90, find the number of articles produced and the cost of each article.

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

At t minutes past 2 pm the time needed by the minutes hand and a clock to show 3 pm was found to be 3 minutes less than Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations minutes. Find t.

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.2

Question 1

The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

John and Jivanti together have 45 marbles. Both of them lost 5 marbles each, and the product of the number of marbles they now have is 128. Form the quadratic equation to find how many marbles they had to start with, if John had x marbles.

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

A cottage industry produces a certain number of toys in a day. The cost of production of each toy (in rupees) was found to be 55 minus the number of articles produced in a day. On a particular day, the total cost of production was Rs. 750. If x denotes the number of toys produced that day, form the quadratic equation to find x.

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

The height of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, form the quadratic equation to find the base of the triangle.

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

An express train takes 1 hour less than a passenger train to travel 132 km between Mysore and Bangalore. If the average speed of the express train is 11 km/hr more than that of the passenger train, form the quadratic equation to find the average speed of express train.

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

A train travels 360 km at a uniform speed. If the speed had been 5 km/hr more, it would have taken 1 hour less for the same journey. Form the quadratic equation to find the speed of the train.

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.3

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

9x2 - 6b2x - (a4 - b4) = 0

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Solve the following quadratic equation by factorisation:

2x2 + ax - a2 = 0

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

Solve the following quadratic equations by factorization:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 32

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 33

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 38

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 43

Solve the following quadratic equations by factorization:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 47

Solve the following quadratic equations by factorization:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Solution 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 48

Solve the following quadratic equations by factorization:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 58

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 59

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 60

Solve the following quadratic equation by factorisation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.4

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.5

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

3x2 - 5x + 2 = 0

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Solve for x:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

Solve for x:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Solve for x:

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.6

Question 1

Determine the nature of the roots of the following quadratic equations:

2x2 - 3x + 5 = 0

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Determine the nature of the roots of the following quadratic equations:

2x2 - 6x + 3 = 0

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Find the values of k for which the roots are real and equal in each of the following equations:

4x2 - 2 (k + 1)x + (k + 1) = 0 

Solution 23

4x2 - 2 (k + 1)x + (k + 1) = 0 Comparing with ax2 + bx + c = 0, we get a = 4, b = -2(k + 1), c = k + 1 According to the question, roots are real and equal. Hence, b2 - 4ac = 0Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

In the following, determine the set of values of k for which the given quadratic equation has real roots:

 

2x2 + x + k = 0

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 32

Find the values of k for which the following equations have real and equal roots:

x2 + k(2x + k - 1) + 2 = 0 

Solution 32

x2 + k(2x + k - 1) + 2 = 0 x2 + 2kx + k(k - 1) + 2 = 0 Comparing with ax2 + bx + c = 0, we get a = 1, b = 2k, c = k(k - 1) + 2 According to the question, roots are real and equal. Hence, b2 - 4ac = 0Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 33

Find the values of k for which the roots are real and equal in each of the following equations:

2x2 + kx + 3 = 0

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

Find the values of k for which the roots are real and equal in each of the following equations:

kx (x - 2) + 6 = 0

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 35

Find the values of k for which the roots are real and equal in each of the following equations:

x2 - 4kx + k = 0

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 36

Find the value of k for which the roots are real and equal in the following equation:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

Find the value of p for which the roots are real and equal in the following equation:

px(x - 3) + 9 = 0

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 38

Find the values of k for which the following equations have real roots.

4x2 + kx + 3 = 0 

Solution 38

4x2 + kx + 3 = 0 Comparing with ax2 + bx + c = 0, we get a = 4, b = k, c = 3 According to the question, roots are real and equal. Hence, b2 - 4ac = 0Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 43

Find the values of k for which the quadratic equation (3k + 1)x2 + 2(k + 1)x + 1 = 0 has equal roots. Also, find the roots.

Solution 43

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 44

Find the values of p for which the quadratic equation (2p + 1)x2 - (7p + 2)x + (7p - 3) = 0 has equal roots. Also, find these roots.

Solution 44

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 45

 If -5 is a root of the quadratic equation, 2x2 + px - 15 = 0, and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k.

Solution 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 46

 If 2 is a root of the quadratic equation 3x2 + px - 8 = 0 and the quadratic equation 4x2 - 2px + k = 0 has equal roots, find the value of k.

Solution 46

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 47

If 1 is root of the quadratic equation 3x2 + ax - 2 = 0 and the quadratic equation a(x2 + 6x) - b = 0 has equal roots, find the value of b.

Solution 47

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 48

Find the value of p for which the quadratic equation (p + 1)x2 - 6(p + 1)x + 3(p + 9) = 0, p -1 has equal roots. Hence, find the roots of equation.

Solution 48

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 49

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 50

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 51

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 52

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 53

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 54

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 55

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 56

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 57

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 58

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 59

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 60

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 61

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 62

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 63

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 63

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 64

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 64

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 65

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 65

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.7

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 11

The sum of a number and its square is 63/4. Find the numbers.

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 24

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 25

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 26

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 28

The difference of the squares of two positive integers is 180. The square of the smaller number is 8 times the larger, find the numbers.

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 29

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 30

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 31

The sum of two numbers is 9. The sum of their reciprocals is 1/2. Find the numbers.

Solution 31

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 32

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 33

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 34

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 35

Find two consecutives odd positive integers, sum of whose squares is 970.

Solution 35

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 36

The difference of two natural numbers is 3 and the difference of their reciprocal is Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations. Find the numbers.

Solution 36

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 37

The sum of the squares of two consecutive odd numbers is 394. Find the numbers.

Solution 37

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 38

The sum of the squares of two consecutive multiples of 7 is 637. Find the multiples.

Solution 38

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 39

The sum of the squares of two consecutive even numbers is 340. Find the numbers.

Solution 39

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 40

The numerator of a fraction is 3 less than the denominator. If 2 is added to both the numerator and the denominator, then the sum of the new fraction and the original fraction isRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations. Find the original fraction.

Solution 40

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations 

Question 41

Find a natural number whose square diminished by 84 is equal to thrice of 8 more than the given number.

Solution 41

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 42

A natural number when increased by 12 equals 160 times its reciprocal. Find the number.

Solution 42

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 4 - Quadratic Equations Exercise Ex. 4.8

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

A train, travelling at a uniform speed for 360 km, would have taken 48 minutes less to travel the same distance if its speed were 5 km/hr more. Find the original speed of the train.

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

A train travels at a certain average speed for a distance 63 km and then travels a distance of 72 km at an average speed of 6 km/hr more than the original speed, If it takes 3 hours to complete total journey, what is its original average speed?

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Concept Insight: Use the relation s =d/t to crack this question and remember here distance is constant so speed and time will vary inversely.

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 12

An aeroplane left 50 minutes later than its scheduled time, and in order to reach the destination, 1250 km away, in time, it had to increase its speed by 250 km/hr from its usual speed. Find its usual speed.

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 13

While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes to reach the destination, 1500 km away in time, the pilot increased the speed by 100 km/hr. Find the original speed/hour of the plane.

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 14

A motor boat whose speed in still water is 18 km/hr takes 1 hour more to go 24 km up stream than to return downstream to the same spot. Find the speed of the stream.

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 15

A car moves a distance of 2592 km with uniform speed. The number of hours taken for the journey is one-half the number representing the speed, in km/hour. Find the time taken to cover the distance.

Solution 15

Let the speed of a car be x km/hr. According to the question, time is Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equationshr. Distance = Speed × Time 2592 = Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic EquationsRd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations x = 72 km/hr Hence, the time taken by a car to cover a distance of 2592 km is 36 hrs.

Chapter 4 - Quadratic Equations Exercise Ex. 4.9

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 8

If Zeba were younger by 5 years than what she really is, then the square of her age (in years) would have been 11 more than 5 times her actual age. What is her age now?

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Question 9

At present Asha's age (in years) is 2 more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age, Asha's age would be one year less than 10 times the present age of Nisha. Find the present ages of both Asha and Nisha.

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations

Chapter 8 - Quadratic Equations Exercise Ex. 8.6

Question 1

Find the value of p for which the roots are real and equal in the following equation:

4x2 + px + 3 = 0

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Quadratic Equations