Question

Solve

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

Answer 1

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

Comparing the given quadratic equation with

$a{x}^2+bx+c=0$ we have

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

$D=b^2-4ac=-34<0$

Hence, the roots will be imaginary.

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

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

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

$=\frac{\sqrt{2}\pm \sqrt{34}i}{2\sqrt{3}}$

Thus $x=\frac{\sqrt{2}+\sqrt{34}i}{2\sqrt{3}}\text{and}x=\frac{\sqrt{2}-\sqrt{34}i}{2\sqrt{3}}$