Question

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

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Answer 1

$\alpha +\beta =-5$

$\alpha \beta =2$

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

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

=25 - 4

=21