Question

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

Answer 1

The given quadratic equation is $\sqrt{3}{x}^2-\sqrt{2}x+3\sqrt{3}=0$
On comparing the given equation with ${ax}^2+bx+c=0$,
we obtain $a=\sqrt{3},b=-\sqrt{2},$ and $c=3\sqrt{3}$
Therefore, the discriminant of the given equation is
$D=b^2-4ac={(-\sqrt{2})}^2-4\left(\sqrt{3}\right)\left(3\sqrt{3}\right)=2-36=-34$
Therefore, the required solutions are
$\frac{-b\pm \sqrt{D}}{2a}=\frac{\sqrt{2}\pm \sqrt{-34}}{2\times \sqrt{3}}=\frac{\sqrt{2}\pm \sqrt{34}i}{2\sqrt{3}}$