Question

Find the value of ${\alpha }^2+{\beta }^2$ if $\alpha ,\beta$ are the roots of $x^2+5x+2=0$

Answer 1

Given: $x^2+5x+2=0$

$\alpha +\beta =-5$

$\alpha \beta =2$

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

$=(-5{)}^2-2\times 2$

$=25-4$

$=21$