Ask a Doubt
Request a call back

Join NOW to get access to exclusive study material for best results

CBSE Class 10 Answered

find k so that x2+2x+k is a factor of 2x4+x3-14x2+5x+6.also,find all zeroes of the polynomial.
Asked by FEHMEEDAH NAZNEEN | 31 Aug, 2010, 09:34: AM
answered-by-expert Expert Answer
Use long division method for the given polynomials as shown below:
 
space space space space space space space space space space space space space space space space space space 2 x squared minus 3 x minus 8 minus 2 k x squared plus 2 x plus k long division enclose 2 x to the power of 4 plus x cubed minus 14 x squared plus 5 x plus 6 end enclose space space space space space space space space space space space space space space space space space space space 2 x to the power of 4 plus 4 x cubed plus 2 k x squared space space space space space space space space space space space space space space space space space space bottom enclose negative space space space space space minus space space space space space minus space space space space space space space space space space space space space space space space space space space end enclose space space space space space space space space space space space space space space space space space space space space space space space space space minus 3 x cubed minus 14 x squared minus 2 k x squared plus 5 x plus 6 space space space space space space space space space space space space space space space space space space space space space space space space space minus 3 x cubed minus 6 x squared space space space space space space space space space space space space space minus 3 k x space space space space space space space space space space space space space space space space space space space space space space space space space space bottom enclose plus space space space space space space plus space space space space space space space space space space space space space space space space space space space plus space space space space space space space space space space end enclose space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 8 x squared minus 2 k x squared plus 5 x plus 3 k x plus 6 space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space minus 8 x squared minus 2 k x squared minus 16 x minus 4 k x minus 8 k minus 2 k squared space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space bottom enclose plus space space space space space space space plus space space space space space space space space plus space space space space space space plus space space space space space space space plus space space space space plus space space space space space space end enclose space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space open parentheses 21 plus 7 k close parentheses x plus 2 k squared plus 8 k plus 6 space space space space space space space space space space space space space space space space space space space space space space
We get the remainder as open parentheses 21 plus 7 k close parentheses x plus 2 k squared plus 8 k plus 6.
Since, x squared plus 2 x plus k is a factor of the given polynomial, the remainder should be zero.
Hence,
21+7k=0 and 2k2+8k+6=0 at the same time.
k= -3 satisfies both equations. Hence, k=-3.
So we can write the polynomial as
2 x to the power of 4 plus x cubed minus 14 x squared plus 5 x plus 6 equals open parentheses x squared plus 2 x minus 3 close parentheses open parentheses 2 x squared minus 3 x minus 2 close parentheses
Hence, the zeroes of x squared plus 2 x minus 3 are
x squared plus 2 x minus 3 equals 0 rightwards double arrow x squared plus 3 x minus x minus 3 equals 0 rightwards double arrow x open parentheses x plus 3 close parentheses minus 1 open parentheses x plus 3 close parentheses equals 0 rightwards double arrow open parentheses x plus 3 close parentheses open parentheses x minus 1 close parentheses equals 0 rightwards double arrow x equals negative 3 space o r space x equals 1
The above two are factors of the 4th degree polynomial as well.
The other two roots of the 4th degree polynomial are roots of the quadratic
2 x squared minus 3 x minus 2 equals 0 rightwards double arrow 2 x squared minus 4 x plus x minus 2 equals 0 rightwards double arrow 2 x open parentheses x minus 2 close parentheses plus 1 open parentheses x minus 2 close parentheses equals 0 rightwards double arrow open parentheses x minus 2 close parentheses open parentheses 2 x plus 1 close parentheses equals 0 rightwards double arrow x equals 2 space o r space x equals negative 1 half
Answered by | 05 May, 2015, 12:04: PM

Application Videos

Concept Videos

Multiple Choice Questions Practice Test
Answered Unanswered My Questions My Answers
CBSE 10 - Maths
The ratio of the sum and product of the roots of the quadratic equation 5x^2 - 6x + 21 + 0 is
Asked by anubhutiupadhaya | 14 Mar, 2024, 11:57: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find the zeroes of the quadratic polynomial 6x²-3x-7x and verify the relationship between zeroes and coefficients.
Asked by reetudetha | 08 Jan, 2024, 04:12: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
if -4 is a zero of the polynomial x^2-2x-(7m+3) then find the value of m
Asked by mysticsurya201 | 04 Jan, 2024, 08:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
the no of polynomial having zeros-2 and 5 is
Asked by fatehbahadurtiwari3 | 30 Dec, 2023, 06:25: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find the zero of the polynomial x²- 55x + 750
Asked by dhaneswarnimal80 | 11 Nov, 2023, 06:50: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find zeros of 4x square -7
Asked by skandachiranjeevin | 01 Nov, 2023, 08:58: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
the value 'p'for which polynomials x²-(p²-9)x+8has zeroes equal in magnitude but opposite in sign is
question image
Asked by sazimkhan178 | 16 Sep, 2023, 11:27: AM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
x²-4x-6 what is the answer
Asked by pranavtamboli65 | 09 Jul, 2023, 09:13: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
p(X)=x2-(k+6)(X+2)(2k-1) then find the value of k is alpha+beta =1/2 alpha beta
Asked by rekhapreetham | 15 Jun, 2023, 08:23: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
CBSE 10 - Maths
find the zeroes of the quadratic polynomial and verify the relationship between the zeroes and the coffiecient 4u+8u
Asked by dimpaldihingia2 | 24 May, 2023, 06:10: PM
ANSWERED BY EXPERT ANSWERED BY EXPERT
My Class Videos Tests ₹ Plans Ask a Doubt
Get Latest Study Material for Academic year 24-25 Click here
×