Question

If $\alpha$ and $\beta$ are the roots of the equation $3x^2-6x+4=0$ find the value of ${\alpha }^2+{\beta }^2$.

Answer 1

Since, $\alpha ,\beta$ are roots of $3x^2-6x+4=0$
$\Rightarrow \alpha +\beta =\frac{6}{3}=2$
$\Rightarrow \alpha \beta =\frac{4}{3}$
Now, ${\alpha }^2+{\beta }^2=(\alpha +\beta {)}^2-2\alpha \beta$
$\Rightarrow {\alpha }^2+{\beta }^2=(2{)}^2-2\times \frac{4}{3}=4-\frac{8}{3}=\frac{4}{3}$