if x2 + x + 1 is a factor of x4 + ax2 + b , then the values of a and b respectively are ???

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.