Question:
Short-Answer Questions
Solve: $2 x^{2}+a x-a^{2}=0$
Solution:
$2 x^{2}+a x-a^{2}=0$
$\Rightarrow 2 x^{2}+2 a x-a x-a^{2}=0$
$\Rightarrow 2 x(x+a)-a(x+a)=0$
$\Rightarrow(x+a)(2 x-a)=0$
$\Rightarrow x+a=0$ 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.
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