Question

Find the values of a and b so that the polynomial f(x) = 2x^3 +ax^2 +bx +6 is divisible by x^2 +x - 2 .

Answer 1

Answer:

a=-2 and b=-6

Step-by-step explanation:

x^2 + x- 2 = 0

x^2 + 2x - x - 2 = 0

x(x+2) - 1(x+2)=0

(x+2)(x-1)=0

x = -2 or x = 1

substituting x as 1,

2 + a + b + 6 = 0

a + b = -8 - 1.

substituting x as -2,

-16-4a - 2b + 6 = 0

4a + 2b = -10 - 2.

subtracting 1. × 2 from 2.,

4a + 2b = -10

- 2a + 2b = -6

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2a = -4

a = -2

substing a as -2 in 1.,

a + b = -8

-2 + b = -8

b = -8+2 = -6