Question

I
If alpha beta are the roots of the equation
x2 + x + 1 = 0
find the value of alpha cube
+ beta cube.​

Answer 1

As; the equation :

f(x) = x² + x + 1 = 0

has roots α = ω and β = ω²; which are the two non real complex cube roots of one

Therefore; α³ + β³ = 1+1 = 2

As,

$\omega ^{3} = 1$

where,

$\omega = \frac{-1±\sqrt{3} i}{2}$