Short-Answer Questions

$2 x^{2}+a x-a^{2}=0$

$\Rightarrow 2 x^{2}+2 a x-a x-a^{2}=0$

$\Rightarrow 2 x(x+a)-a(x+a)=0$

$\Rightarrow(x+a)(2 x-a)=0$

$\Rightarrow x+a=0$ or $2 x-a=0$

$\Rightarrow x=-a$ or $x=\frac{a}{2}$

Hence, $-a$ and $\frac{a}{2}$ are the roots of the given equation.