Solve the following equations by factorisation:

2x² + ax - a² = 0

Given,

$\Rightarrow 2x^2 + ax - a^2 = 0 \\[1em] \Rightarrow 2x^2 + 2ax - ax - a^2 = 0 \\[1em] \Rightarrow 2x(x + a) - a(x + a) = 0 \\[1em] \Rightarrow (x + a)(2x - a) = 0 \\[1em] \Rightarrow x + a = 0 \text{ or } 2x - a = 0 \\[1em] \Rightarrow x = -a \text{ or } x = \dfrac{a}{2}$

Hence, roots of given equation are $-a, \dfrac{a}{2}$.