Question

Solve

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

Answer 1

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

Comparing the given quadratic equation with

$a{x}^2+bx+c=0$ 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 $x=\frac{-1-\sqrt{7}i}{2\sqrt{2}}$