If the sum of the roots of a quadratic equation is $1$ and the sum of the squares of the roots is $13$,then find the equation.

If the ratio of the roots of the equation $ax^2 + bx + c = 0$ is $p:q$,then

If $a(p + q)^2 + 2bpq + c = 0$ and $a(p + r)^2 + 2bpr + c = 0$,then $qr$ =

Let $A = \left| \begin{matrix} 2 & e^{i \pi} \\ -1 & i^{2012} \end{matrix} \right|$,$C = \left. \frac{d}{dx} \left( \frac{1}{x} \right) \right|_{x=1}$,and $D = \int_{e^2}^{1} \frac{dx}{x}$. If the sum of two roots of the equation $Ax^3 + Bx^2 + Cx - D = 0$ is equal to zero,then $B$ is equal to:

If $\alpha, \beta$ are the roots of the equation $lx^2 + mx + n = 0$,then the equation whose roots are $\alpha^3\beta$ and $\alpha\beta^3$ is

For the quadratic equation $2x^2 - (p + 1)x + (p - 1) = 0$,if $\alpha - \beta = \alpha \beta$,then what is the value of $p$?