The value of m( $k =$ $m a^{2}$ ) for which the given value is a solution of the given equation :
$x^{2} + 3 a x + k = 0, x = - a$ is

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Solution

$x^{2} + 3 a x + k = 0$
Substituting $x = - a$ ,
$\Rightarrow$ $(- a)^{2} + 3 a (- a) + k = 0$
$\Rightarrow$ $a^{2} - 3 a^{2} + k = 0$
$\Rightarrow$ $- 2 a^{2} + k = 0$
$\Rightarrow$ $k = 2 a^{2}$
Now substituting $k = m a^{2}$
$\Rightarrow$ $m a^{2} = 2 a^{2}$
$∴$ $m = 2$

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