The quadratic equation $2x^{2} - \sqrt{5}x + 1 = 0$ has

Find the roots of the following quadratic equation,if they exist,using the quadratic formula: $2x^2 - 2\sqrt{2}x + 1 = 0$.

Obtain the roots of the following quadratic equation by using the general formula for the solution: $2x^{2} - 2\sqrt{2}x + 1 = 0$.

If the value of the discriminant of the quadratic equation $2x^{2} + 5x - k = 0$ is $81$,then $k = \dots$

Find the discriminant of the following quadratic equation and hence determine the nature of its roots: $x^{2}-2 \sqrt{2} x+1=0$

State whether the quadratic equation $\sqrt{2} x^{2}-\frac{3}{\sqrt{2}} x + \frac{1}{\sqrt{2}} = 0$ has two distinct real roots. Justify your answer.