Math, asked by ramanaputturu123, 9 months ago

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Answered by abhinay365

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$\boxed{Answer:-}$

Given equation

${x}^{2} + 3ax + 2 {a}^{2} = 0$

Given alpha and beta are the roots.

${ \alpha }^{2} + { \beta }^{2} = 5$

We know

${ \alpha }^{2} + { \beta }^{2} =( { \alpha + \beta })^{2} - 2 \alpha \beta \\ 5 = ({ \frac{ - b}{a} })^{2} - 2( \frac{c}{a} ) \\ 5= ({ \frac{3a}{1} })^{2} - 2(2 {a}^{2} ) \\ 5 = 9 {a}^{2} - 4 {a}^{2} \\ 5 = 5 {a}^{2} \\ {a}^{2} = 1 \\ a = 1 \: or \: a = - 1$

Hence a values are 1 and -1

Hope it helps! ! ! !

Mark my answer as brainliest! ! ! !

Regards,

Abhinay.

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