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