Question

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

Answer 1

For the quadratic equation $a{x}^2+bx+c=0$ , the roots are given by

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

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

$b^2-4ac=(1{)}^2-4(\sqrt{2}\left)\right(\sqrt{2})=-7$

So, the roots are

$x=\frac{-1\pm \sqrt{-7}}{2\sqrt{2}}$

$x=\frac{-1\pm \sqrt{7}i}{2\sqrt{2}}$