If the following quadratic equation has two equal and real roots,then find the value of $k$: $5x^{2} - 2kx + 20 = 0$.

Find the roots of the following quadratic equation by the method of completing the square: $2x^{2} + x + 4 = 0$.

Find the discriminant of the following quadratic equation and hence determine the nature of the roots of the equation: $5x^{2} - 4\sqrt{5}x + 4 = 0$.

The standard form of a quadratic equation in one variable is $\ldots \ldots \ldots \ldots . .$

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 .....

At present,Asha's age (in $years$) is $2$ more than the square of her daughter Nisha's age. When Nisha grows to her mother's present age,Asha's age would be one year less than $10$ times the present age of Nisha. Find the present ages of both Asha and Nisha (in $years$).