Question

Solve following equation:
$\sqrt{3}{x}^2-2\sqrt{3}x+3\sqrt{3}=0$

Answer 1

For the quadratic equation $a{x}^2+bx+c=0$ , the roots are given by

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For the equation $\sqrt{3}{x}^2-2\sqrt{3}x+3\sqrt{3}=0$ ,

$b^2-4ac={(-2\sqrt{3})}^2-4\left(\sqrt{3}\right)\left(3\sqrt{3}\right)$

$=12-36=-24$

So, the roots are

$x=\frac{2\sqrt{3}\pm \sqrt{-24}}{2\sqrt{3}}$

$x=\frac{2\sqrt{3}\pm 2\sqrt{6}i}{2\sqrt{3}}$

$x=1\pm \sqrt{2}i$