If the following quadratic equation has two equal and real roots,then find the value of $k$: $x^{2} + 2kx + 4 = 0$.

State whether the following statement is 'True' or 'False'. Justify your answer: If in a quadratic equation the coefficient of $x$ is zero,then the quadratic equation has no real roots.

The formula for finding the value of $D$ (discriminant) for a quadratic equation $ax^2 + bx + c = 0$ is $\ldots \ldots \ldots \ldots.$

Which of the following equations has two distinct real roots?

In quadratic equation $ax^{2} + bx + c = 0$,where $a \neq 0$,$b = 0$,and $D > 0$,then both the roots of the equation are .....

If the value of the discriminant of the quadratic equation $x^{2} + \sqrt{2}x + 2 = 0$ is .... .