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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 $\frac{b}{a}$. 
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