We have , $x^2 + \frac{x}{\sqrt{2}}$ + 1 = 0 Comparing the given equation with the general form $ax^2$ + bx + c = 0, we get a = 1 , b = $\frac{1}{\sqrt{2}}$ , c = 1 ∴ x = $\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ = $\frac{-\frac{1}{\sqrt{2}} \pm \sqrt{\left(\frac{1}{\sqrt{2}}\right)^2 - 4 \times 1 \times 1}}{2.1}$ = $\frac{-\frac{1}{\sqrt{2}} + \sqrt{\frac{1}{2} - 4}}{2}$ = $\frac{-\frac{1}{2} \pm \sqrt{\frac{1 - 8}{2}}}{2}$ = $\frac{-\frac{1}{\sqrt{2}} \pm \sqrt{-\frac{7}{2}}}{2}$ = $\frac{-1 \pm i\sqrt{7}}{2\sqrt{2}}$ ∴ The roots of the given equation are $\frac{-1 + i\sqrt{7}}{2\sqrt{2}}$ and $\frac{-1 - i\sqrt{7}}{2\sqrt{2}}$