Question

If $\alpha ,\beta$ be the roots of $x^2–x+3=0$, then the value of $({\omega }^2\alpha +\omega \beta )(\omega \alpha +{\omega }^2\beta )$ is, ($\omega$ is complex cube root of unity)

• A. $-6$
• B. $-1$
• C. $1$
• D. $-8$

Answer 1

The correct option is D $-8$

$\alpha +\beta =1\alpha \beta =3$
$({\omega }^2\alpha +\omega \beta )(\omega \alpha +{\omega }^2\beta )={\alpha }^2+{\beta }^2+\alpha \omega ({\omega }^2+\omega )$
$={\alpha }^2+{\beta }^2-\alpha \beta$
$=(\alpha +\beta {)}^2-3\alpha \beta$
$=1-9$
$=-8$