Question

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

Answer 1

Given: $\sqrt{3}{x}^2-\sqrt{2}x+3\sqrt{3}=0$

Solution of a quadratic equation, $a{x}^2+bx+c=0$ is given as

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

On comparing $\sqrt{3}{x}^2-\sqrt{2}x+3\sqrt{3}=0$ with $a{x}^2+bx+c=0$

we get, $a=\sqrt{3},b=-\sqrt{2}$ and $c=3\sqrt{3}$

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

$=\frac{\sqrt{2}\pm \sqrt{2-36}}{2\sqrt{3}}$

$x=\frac{\sqrt{2}\pm \sqrt{-34}}{2\sqrt{3}}$

$x=\frac{\sqrt{2}\pm i\sqrt{34}}{2\sqrt{3}}$ $[\because \sqrt{-1}=i]$

$\therefore$ roots are $\frac{\sqrt{2}+i\sqrt{34}}{2\sqrt{3}}$ and $\frac{\sqrt{2}-i\sqrt{34}}{2\sqrt{3}}$