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

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $9x^{2} - 5x + 3 = 0$.

Find the roots of the following quadratic equation by using the quadratic formula,if they exist: $x^{2}-5x-1=0$

The difference between the lengths of the sides of a right triangle which form the right angle is $7 \, cm$. If its perimeter is $30 \, cm$,find the lengths of the sides.

If $-3$ is a root of a quadratic equation $x^{2}+3(k+2)x-9=0$,then $k=\ldots \ldots \ldots \ldots .$

Which of the following is true for the coefficients and constant term of a quadratic equation $ax^2 + bx + c = 0$?