Question

If a,b, g, d are the roots of the equation x⁴ + x³ + x² + x +1 = 0, then a²⁰²¹ + b²⁰²¹ + g²⁰²¹ + d²⁰²¹ is equal to:

(A) –4

(B) –1

(C) 1

(D) 4

Answer 1

Correct option is (B) –1

α, β, γ, δ root of the equation 

x⁴ + x³ + x² + x + 1 = 0 

Which are 5^th roots of unity except 1.

then a²⁰²¹ + b²⁰²¹ + g²⁰²¹ + d²⁰²¹ = α + β + γ + δ = -1