Request a call back

# CBSE Class 10 Answered

Solve :
Asked by shankaranarayanan | 23 Feb, 2011, 09:15: PM Expert Answer
Dear Student,
Let us take the general form of a quadratic equation:

ax2 + bx + c = 0     [a ≠ 0 ]                      (1)

If and ß be the roots of the equation (1), then = and ß = Now, suppose that a, b and c are real and rational. Then, the nature of the roots and ß of
equation (1) is determinedby the expression (b2 – 4ac) under the radical sign.

Therefore (b2 – 4ac) is known as the Discriminant of equation (1). Referred to this discriminant following conclusions can be drawn about the nature of roots and ß of equation (1):

1. If discriminant is positive (that is, if b2 – 4ac > 0), then the roots and ß of equation (1) are real andunequal.

2. If discriminant is zero (that is, if b2 – 4ac = 0), then the roots and ß of equation (1) are real and equal
3. If discriminant is negative (that is, if b2 – 4ac < 0), then the roots and ß of equation (1) are imaginary and unequal
4. If discriminant is positive and a perfect square then the roots of equation (1) are real, rational and unequal. And if the discriminant is positive but not a perfect square then the roots of equation (1) are real, irrational and unequal.
5. If b2 – 4ac is a perfect square but any one of a or b is irrational then the roots of equation (1) are irrational.

Now, here if c is < 0 it means it is a negative digit then discriminant (b2-4ac) becomes positive. Hence the nature of roots will either follow point (1) or point(4) mentioned above.

Regards

Team Topperlearning

Answered by | 23 Feb, 2011, 07:34: PM

## Application Videos

CBSE 10 - Maths
Asked by Subuhiansari67 | 28 Sep, 2022, 10:11: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by devchauhan25007 | 17 Jul, 2022, 04:29: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by rajendrame089 | 28 Jun, 2022, 07:09: AM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by gurjaeharsh | 16 Jun, 2022, 01:11: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by geetayadav18081983 | 15 Jun, 2022, 01:19: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by atharvsharma971 | 06 Jun, 2022, 10:30: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by harshitpranjalraj24 | 03 Jun, 2022, 09:33: PM ANSWERED BY EXPERT
CBSE 10 - Maths
1,2&3 Asked by zk4656260 | 31 May, 2022, 05:32: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by s.kmounesha | 23 May, 2022, 02:35: PM ANSWERED BY EXPERT
CBSE 10 - Maths
Asked by ankur.spsharma | 02 May, 2022, 11:54: AM ANSWERED BY EXPERT