Solve the Quadratic Equation by Factorization: a²x² − 3abx + 2b² = 0

Question: Solve the following quadratic equation by factorization:

$$ a^2x^2-3abx+2b^2=0 $$

Solution

$$ a^2x^2-2abx-abx+2b^2=0 $$

$$ ax(ax-2b)-b(ax-2b)=0 $$

$$ (ax-2b)(ax-b)=0 $$

Either

$$ ax-2b=0 $$

$$ x=\frac{2b}{a} $$

or

$$ ax-b=0 $$

$$ x=\frac{b}{a} $$

Hence,

$$ \boxed{x=\frac{2b}{a},\ \frac{b}{a}} $$