Question

Find the roots of the quadratic equations given in Q.1 above by applying the quadratic formula.
(iii) $4x^2+4\sqrt{3}x+3=0$

Answer 1

(iii) $4x^2+4\sqrt{3}x+3=0$
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}$
$\Rightarrow$ $x=\frac{-4\sqrt{3}\pm \sqrt{48-48}}{8}$
$\Rightarrow$ $x=\frac{-4\sqrt{3}\pm \sqrt{0}}{8}$
$\Rightarrow$ $x=\frac{-4\sqrt{3}}{8}$
$\therefore x=\frac{\sqrt{3}}{2}orx=-\frac{\sqrt{3}}{2}$