Question

Solve the quadratic equation $2x^2+ax-a^2=0$ for $x$.

Answer 1

Factorize the given equation

Given that,

$2x^2+ax-a^2=0$

$$\begin{gathered} \Rightarrow 2x^2+2ax–ax–a^2=0 \\ \Rightarrow 2x(x+a)–a(x+a)=0 \\ \Rightarrow (x+a)(2x–a)=0 \\ \text{Either},x+a=0\text{or}(2x–a)=0 \\ \Rightarrow x=-a\text{or}x=\frac{a}{2} \end{gathered}$$

Hence, $\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\mathbf{-}\mathit{a}\mathbf{}\mathbf{\text{or}}\mathbf{}\mathit{x}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{a}}{\mathbf{2}}$ are the solution of given quadratic equation.