Question

Short-Answer Questions

Solve: $2x^2+ax-a^2=0$ [CBSE 2014]

Answer 1

$$\begin{gathered} 2x^2+ax-a^2=0 \\ \Rightarrow 2x^2+2ax-ax-a^2=0 \\ \Rightarrow 2x\left(x+a\right)-a\left(x+a\right)=0 \\ \Rightarrow \left(x+a\right)\left(2x-a\right)=0 \end{gathered}$$
$$\begin{gathered} \Rightarrow x+a=0\mathrm{or}2x-a=0 \\ \Rightarrow x=-a\mathrm{or}x=\frac{a}{2} \end{gathered}$$

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