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: $9x^{2} - 5x + 3 = 0$.

If one root of $x^{2}-5x+6=0$ is also the root of $x^{2}+3x+c=0$,then $c = \ldots$

If one of the roots of the equation $px^{2} + qx + r = 0$ where $p \neq 0$ and $p, q, r \in R$ is $x = -2$,then prove that $4p - 2q + r = 0$.

Which of the following is a quadratic equation in one variable?

We get $2$ litres of kerosene less in Rs. $360$ if the price of kerosene increases by Rs. $2$ per litre. Find the original price of kerosene per litre.