Question

Find the roots of the following quadratic equation by factorization.
${4x}^2-12x+9=0$
$4\sqrt{{3x}^2}+5x-2\sqrt{3}=0$

Answer 1

$4x^2-12x+9=0$

$\Rightarrow$ $4x^2-6x-6x+9=0$

$\Rightarrow$ $2x(2x-3)-3(2x-3)=0$

$\Rightarrow$ $(2x-3)(2x-3)=0$

$\Rightarrow$ $2x-3=0$ and $2x-3=0$

$\therefore$ $x=\frac{3}{2}$ and $x=\frac{3}{2}$

$4\sqrt{3}{x}^2+5x-2\sqrt{3}=0$

$\Rightarrow$ $4\sqrt{3}{x}^2+8x-3x-2\sqrt{3}=0$

$\Rightarrow$ $4x(\sqrt{3}x+2)-\sqrt{3}(\sqrt{3}x+2)=0$

$\Rightarrow$ $(\sqrt{3}x+2)(4x-\sqrt{3})=0$

$\Rightarrow$ $x=\frac{-2}{\sqrt{3}}$ and $x=\frac{\sqrt{3}}{4}$