Question

Let $\alpha ,\beta$ are the roots of $4x^2+3x-9=0$
Then find ${\alpha }^2+{\beta }^2$

Answer 1

$4x^2+3x-9=0$

$\alpha +\beta =\frac{-b}{a}=\frac{-3}{4}$

$\alpha \beta =\frac{c}{a}=\frac{-9}{4}$

$\left(i\right){\alpha }^2+{\beta }^2={\alpha }^2+{\beta }^2+2\alpha \beta -2\alpha \beta$

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

$={\left(\frac{-3}{4}\right)}^2-2\times \frac{-9}{4}$

$=\frac{9}{16}+\frac{18}{4}$

$=\frac{81}{16}$