Question

if the polynomial x^2-x-6 divides the polynomial x^4+ax-b exactly, then find the values of a and b.​

Answer 1

Step-by-step explanation:

Find the roots of

{x}^{2} - 3x + 2

then place these values in the second polynomial,you will get two equation,solve them for calculating a and b.

{x}^{2} - 3x + 2 = 0 \\ {x}^{2} - 2x - x + 2 = 0 \\ x(x - 2) - 1(x - 2) = 0 \\ (x - 2)(x - 1) = 0 \\ x - 2 = 0 \\ x = 2 \\ x - 1 = 0 \\ x = 1

put x = 2

{x}^{3} - 6 {x}^{2} + ax + b = 0 \\ 8 - 6(4) + 2a + b = 0 \\ 8 - 24 + 2a + b = 0 \\ 2a + b = 16

put x= 1

{x}^{3} - 6 {x}^{2} + ax + b = 0 \\ 1 - 6 + a + b = 0 \\ a + b = 5

subtract both equations

2a - a \: = 16 - 5 \\ a = 11

a + b = 5 \\ 11 + b = 5 \\ b = 5 - 11 \\ b = - 6

hope it's help you

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