Question

x2+x+1=0 is the factor of x4+ax2+b find a and b

Answer 1

Answer:

Divide f(x) = x4 + ax2 + b by g(x) = x2 + x + 1.

Given, g(x) = x2 + x + 1 is a factor of f(x) = x4 + ax2 + b.

∴ Remainder = (1 – a) x + (b – a) = 0 = 0x + 0

Comparing coefficient of x and constant term on both sides, we have

1 – a = 0

⇒ a = 1

and b – a = 0

⇒ b = a

⇒ b = 1

Hence, the value of a is 1 and b is 1.

Step-by-step explanation:

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