Question

If x2 + x + 1 is a factor of x4 + ax2 + b, then find the values of a and b.

Answer 1

Answer:

x^2 - 3x + 2 = (x - 2)(x - 1)

x = 1, x = 2 make f(x) zero :

x = 1,

1^4 - a(1)^3 + b = 0

a - b = 1

x = 2,

2^4 - a(2)^3 + b = 0

16 - 8a + b = 0

-8a + b = -16

=>

a - b = 1

-8a + b = -16

a = 15/7, b = 8/7

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Step-by-step explanation:

Answer 2

as now taking x as coefficient so what we get is that.

1-a = 0 thus, a=1

b-a =0 thus, b=a

so the answer is that

a =1 as well as b =1.