Question

Find the roots of the following quadratic equations, if they exist, by the method of completing the square:
$4x^2+4\sqrt{3}x+3=0$

Answer 1

$4x^2+4\sqrt{3}x+3=0$
We know;
D = $b^2–4ac$
= $(4\sqrt{3}{)}^2–4\times 4\times 3$
= 48 - 48
= 0
Since, $D=0$, hence roots are possible for this equation.
$\Rightarrow$ $(2x{)}^2+2\times 2x\times \sqrt{3}+(\sqrt{3}{)}^2=0$
$\Rightarrow$ $(2x+\sqrt{3}{)}^2=0$
$\Rightarrow$ $(2x+\sqrt{3})=0and(2x+\sqrt{3})=0$
$\Rightarrow$ $x=-\frac{\sqrt{3}}{2}orx=-\frac{\sqrt{3}}{2}$