Question

If $\alpha ,\beta ,\gamma$ are the roots of the equation $2x^3-x^2+x-1=0$, then ${\alpha }^2+{\beta }^2+{\gamma }^2=$

• A. $\frac{5}{4}$
• B. $\frac{3}{4}$
• C. $\frac{-5}{4}$
• D. $\frac{-3}{4}$

Answer 1

The correct option is D $\frac{-3}{4}$

${\alpha }^2+{\beta }^2+{\gamma }^2={(\alpha +\beta +\gamma )}^2-2(\alpha \beta +\beta \gamma +\gamma \alpha )$

$=s_1^2-2s_2=\frac{1}{4}-2\times \frac{1}{2}$

$=\frac{-3}{4}$