Question

Find the roots of the following quadratic equation:
$2\sqrt{3}{x}^2-5x+\sqrt{3}=0$

Answer 1

The given quadratic equation is $2\sqrt{3}{x}^2-5x+\sqrt{3}=0$
Comparing with the standard from $a{x}^2+bx+c=0$
The value of a, b and c are
$a=2\sqrt{3},b=-5,c=\sqrt{3}$
$\sqrt{D}=\sqrt{b^2-4ac}=\sqrt{25-4\times 2\sqrt{3}\times \sqrt{3}}$
$=\sqrt{25-24}=\sqrt{1}=1$
$\therefore x=\frac{-b\pm \sqrt{D}}{2a}$
$=\frac{5\pm 1}{2\times 2\sqrt{3}}$
$=\frac{6}{4\sqrt{3}}or\frac{4}{4\sqrt{3}}$
$=\frac{3}{2\sqrt{3}}or\frac{1}{\sqrt{3}}$
$=\frac{\sqrt{3}}{2}or\frac{\sqrt{3}}{3}$
Therefore, the roots of the given quadradic equation are $\frac{\sqrt{3}}{2}and\frac{\sqrt{3}}{3}$