Question

Solve the following quadratic equations by factorization:

\[2x^2 + ax - a^2 = 0\]

Solve for x:

\[2x^2 + ax - a^2 = 0\]

Answer 1

\[2 x^2 + ax - a^2 = 0\]

\[ \Rightarrow 2 x^2 + 2ax - ax - a^2 = 0\]

\[ \Rightarrow 2x\left( x + a \right) - a\left( x + a \right) = 0\]

\[ \Rightarrow \left( 2x - a \right)\left( x + a \right) = 0\]

\[ \Rightarrow 2x - a = 0 \text { or } x + a = 0\]

\[ \Rightarrow x = \frac{a}{2} \text { or } x = - a\]

Hence, the factors are \[\frac{a}{2}\] and \[- a\].