Solve 3 x^2 - 2 x + 3 3 = 0 - Vidyadip

Question

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

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Answer

Here $\sqrt 3 {x^2} - \sqrt 2 x + 3\sqrt 3 = 0$
Comparing the given quadratic equation with $ax^2 + bx + c = 0$ we have
$a = \sqrt 3 ,b = - \sqrt 2 $ and $c = 3\sqrt 3 $
$\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 { - 34} }}{{2\sqrt 3 }}$.
$ = \frac{{\sqrt 2 \pm \sqrt { 34} i}}{{2\sqrt 3 }}$
Thus $x = \frac{{\sqrt 2 + \sqrt {34} i}}{{2\sqrt 3 }}$ and $x = \frac{{\sqrt 2 - \sqrt {34} i}}{{2\sqrt 3 }}$.

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