Question

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

Answer 1

Solve for the required roots:

Given quadratic equation is $4x^2+4\sqrt{3}x+3=0$

According to the quadratic formula for a quadratic equation $a{x}^2+bx+c=0$, $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here $a=4,b=4\sqrt{3},c=3$

$\therefore$$x=\frac{-4\sqrt{3}\pm \sqrt{{\left(4\sqrt{3}\right)}^2-4\left(4\right)\left(3\right)}}{2\left(4\right)}$

$\begin{array}{cl}=& \frac{-4\sqrt{3}\pm \sqrt{48-48}}{8}\\ =& \frac{-4\sqrt{3}}{8}\\ =& \frac{-\sqrt{3}}{2}\end{array}$

Hence the required roots of the given quadratic equation are $\frac{-\sqrt{3}}{2},\frac{-\sqrt{3}}{2}$