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

Question

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

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Answer

Here $\sqrt 2 \;{x^2} + x + \sqrt 2 = 0$
Comparing the given quadratic equation with $ax^2 + bx + c = 0$ we have
$a = \sqrt 2 $, b = 1 and $c = \sqrt 2 $
$\therefore x = \frac{{ - 1 \pm \sqrt {{{(1)}^2} - 4 \times \sqrt 2 \times \sqrt 2 } }}{{2 \times \sqrt 2 }}$$ = \frac{{ - 1 \pm \sqrt { - 7} }}{{2\sqrt 2 }} = \frac{{ - 1 \pm \sqrt 7 i}}{{2\sqrt 2 }}$
Thus $x = \frac{{ - 1 + \sqrt 7 i}}{{2\sqrt 2 }}$ and $x = \frac{{ - 1 - \sqrt 7 i}}{{2\sqrt 2 }}$

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