If α and β are roots of the equation x2 + x + 1 = 0 then α2 + β2 is

Question

If α and β are roots of the equation x2 + x + 1 = 0 then α2 + β2 is (A) ( - 1 - i √3/2) (B) 1 (C) -1 (D) ( - 1 + i √3/2)

Tardigrade Admin · Accepted Answer

x2+x+1=0 ⇒ x=α, β=α2 where α is the cube root of unity α2+β2=ω2+ω4 =ω2+ω =-1

Q. If $α$ and $β$ are roots of the equation $x^{2} + x + 1 = 0$ then $α^{2} + β^{2}$ is