Question
Solve the following quadratic equation by factorisation:
$2x^2 + ax - a^2 = 0$ where $a ∈ R.$
$2x^2 + ax - a^2 = 0$ where $a ∈ R.$
✓
Answer
$2 x^2+a x-a^2=0$
$ \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 \text { or } 2 x-a=0$
$ \Rightarrow x=-a \text { and } x=\frac{a}{2} .$
$ \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 \text { or } 2 x-a=0$
$ \Rightarrow x=-a \text { and } x=\frac{a}{2} .$
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