Question

please answer this question fast

Answer 1

QUESTION:

For polynomials p(x) = 6x³ + 11x² + kx - 20 and q(x) = 9x² - 5x , x = 2 is a root of the polynomial (p(x) + q(x)). Then find the value of k.

ANSWER:

• The value of k = - 49

GIVEN:

• p(x) = 6x³ + 11x² + kx - 20

• q(x) = 9x ² - 5x

• x = 2 is a root of the polynomial (p(x) + q(x))

TO FIND:

• The value of k.

EXPLANATION:

p(x) + q(x) = 6x³ + 11x² + kx - 20 + 9x ² - 5x

p(x) + q(x) = 6x³ + 20x² + (k - 5)x - 20

x = 2 is a root of the polynomial p(x) + q(x).

p(2) + q(2) = 0

6(2³) + 20(2²) + (k - 5)2 - 20 = 0

6(8) + 20(4) + 2k - 10 - 20 = 0

48 + 80 + 2k - 30 = 0

2k + 80 + 18 = 0

2k + 98 = 0

k + 49 = 0

k = - 49

HENCE THE VALUE OF K = - 49