Question

Find the roots of the following equation applying quadratic formula.
$4x^2+4\sqrt{3}x+3=0$

• A. $-\frac{\sqrt{3}}{2}$ and $-\frac{\sqrt{3}}{2}$
• B. $\frac{\sqrt{3}}{2}$ and $-\frac{\sqrt{3}}{2}$
• C. $\frac{4\sqrt{3}}{8}$ and $\frac{\sqrt{3}}{2}$
• D. $\frac{-3\sqrt{3}}{8}$ and $\frac{\sqrt{3}}{2}$

Answer 1

The correct option is A

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

$4x^2+4\sqrt{3}x+3=0$
On comparing this equation with $a{x}^2+bx+c=0$, we get
$a=4,b=4\sqrt{3}andc=3$
By using quadratic formula, we get
$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$
$\Rightarrow$$x=\frac{-4\sqrt{3}\pm \sqrt{(4\sqrt{3}{)}^2-4\times 4\times 3}}{2\times 4}$
$\Rightarrow$ $x=\frac{-4\sqrt{3}\pm \sqrt{48-48}}{8}$
$\Rightarrow$ $x=\frac{-4\sqrt{3}\pm \sqrt{0}}{8}$
$\Rightarrow$ $x=\frac{-4\sqrt{3}}{8}$
$\therefore x=-\frac{\sqrt{3}}{2}$

Thus, the given quadratic equation has equal roots.