Question

Find the roots of the following quadratic equation by the method of completing the square.
$4x^2+4\sqrt{3}x+3=0$

• A. $-\frac{\sqrt{3}}{2}and-\frac{\sqrt{3}}{2}$
• B. $-\frac{\sqrt{5}}{2}and-\frac{\sqrt{5}}{2}$
• C. $-\frac{1}{\sqrt{3}}and-\frac{1}{\sqrt{3}}$
• D. $-\frac{2}{\sqrt{3}}and-\frac{2}{\sqrt{3}}$

Answer 1

The correct option is A

$-\frac{\sqrt{3}}{2}and-\frac{\sqrt{3}}{2}$

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

$\Rightarrow$ $(2x{)}^2+2\times 2x\times \sqrt{3}+(\sqrt{3}{)}^2=0$

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

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

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

Therefore, the given equation has equal roots.