Solve the following quadratic equation by factorization:
$a^2x^2\ –\ 3abx\ +\ 2b^2\ =\ 0$

Given:

Given quadratic equation is $a^2x^2\ –\ 3abx\ +\ 2b^2\ =\ 0$.

To do:

We have to solve the given quadratic equation by factorization. 

Solution:

$a^2x^2\ –\ 3abx\ +\ 2b^2\ =\ 0$

$a^2x^2-2abx-abx+2b^2=0$ 

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

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

$ax-2b=0$ or $ax-b=0$

$ax=2b$ or $ax=b$

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

The roots of the given quadratic equation are $\frac{2b}{a}$ and $\frac{b}{a}$.