Question

Solve the equation $x^2+\frac{x}{\sqrt{2}}+1=0$

Answer 1

The given quadratic equation is $x^2+\frac{x}{\sqrt{2}}+1=0$
This equation can also be written as $\sqrt{2}{x}^2+x+\sqrt{2}=0$
On comparing the given equation with ${ax}^2+bx+c=0$,
we obtain $a=\sqrt{2},b=1,$ and $c=\sqrt{2}$
$\therefore$ discriminant $D=b^2-4ac=1^2-4\sqrt{2}\times \sqrt{2}=1-8=-7$
Therefore, the required solutions are
$\frac{-b\pm \sqrt{D}}{2a}=\frac{-1\pm \sqrt{-7}}{2\sqrt{2}}=\frac{-1\pm \sqrt{7i}}{2\sqrt{2}}$