Question

For which values of a and b, the zeroes of q(x) = x 3 – 2x 2 – x + a are also the zeroes of the polynomial p(x) = x 5 – 2x 4 – 10x 3 + 20x 2 + 9x + b?

Answer 1

For which values of a and b, the zeroes of q(x) = x 3 – 2x 2 – x + a are also the zeroes of the polynomial p(x) = x 5 – 2x 4 – 10x 3 + 20x 2 + 9x + b?

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Answer 2

Step-by-step explanation:

Given For which values of a and b, the zeroes of q(x) = x 3 – 2x 2 – x + a are also the zeroes of the polynomial p(x) = x 5 – 2x 4 – 10x 3 + 20x 2 + 9x + b?

• Now by division algorithm we get
•    So x^3 – 2x^2 – x + a ) x^5 – 2x^4 – 10 x^3 + 20x^2 + 9x + b (x^2 – 9
•                                    So    x^5 – 2x^4 – x^3 + ax^2
•                                                    So      - 9x^3 + (20 – a) x^2 + 9x + b
•                                                      So    - 9x^3 + 18 x^2 + 9x – 9a
•                                                                           (20 – a – 18) x^2 + (b + 9a)
•                                 So (2 – a) x^2 + (b + 9a)
• So if (x^2 – 9) is a factor of x^5 – 2x^4 – 10 x^3 + 20 x^2 + 9x + b then remainder should be zero.
• So we can take 2 – a = 0
•                 Or a = 2
• Also b + 9a = 0
•       Or b + 9(2) = 0
•      Or b = - 18
• So q(x) = x^3 – 2x^2 – x + 2
• So p(x) = x^5 – 2x^4 – 10x^3 + 20x^2 + 9x – 18
•          = (x^3 – 2x^2 – x + 2) (x^2 – 9) + 0
•          = (x^3 – 2x^2 – x + 2) (x + 3) (x – 3)
• So the other zeroes of p(x) are – 3 and 3

Reference link will be

https://brainly.in/question/16765837