Question

If $\alpha$ and $\beta$ are zeros of the quadratic polynomial $2x^2+3x-6$, then find the values of :
${\alpha }^2+{\beta }^2$

• A. $\frac{35}{4}$
• B. $\frac{25}{9}$
• C. $\frac{24}{7}$
• D. $\frac{22}{9}$

Answer 1

The correct option is A $\frac{35}{4}$

${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta =(\frac{-3}{2}{)}^2-2\left(\frac{-6}{2}\right)=\left(\frac{9}{4}\right)+6=\left(\frac{9+24}{4}\right)=\left(\frac{35}{4}\right)$