Question

If \( \alpha \) and \( \beta \) are the roots of the equation \( x^{2}-x+1=0 \), then \( \alpha^{2009}+\beta^{2009}= \) 

(1) -2 

(2) -1 

(3) 1 

(4) 2

Answer 1

x³ + 1 = (x + 1)(x² − x + 1)

So, since α is a root of x² − x + 1 = 0 we have,