Question

If α, β, γ, δ are the roots of the equation x 4 + x 3 + x 2 + x + 1 = 0, then α2021 + β2021 + γ2021 + δ2021 is equal to

• A. -4
• B. -1
• C. 1
• D. 4

Answer 1

Answer: (B)

-1

Answer 2

x4 + x3 + x2 + x + 1 = 0 or $\frac{x^5-1}{x-1}$ = 0.
So roots are e$^{\frac{i2\pi}{5}}$, e$^{\frac{i4\pi}{5}}$, e$^{\frac{i6\pi}{5}}$, e$^{\frac{i8\pi}{5}}$, i.e. α,β,γ and δ
From properties of n th root of unity
$1^{2021}+α^{2021}+β^{2021}+γ^{2021}+δ^{2021}$=0
⇒ $α^{2021}+β^{2021}+γ^{2021}+δ^{2021}=-1$