If $\alpha$ and $\beta$ are roots of the equation $Ax^2 + Bx + C = 0$,then the value of $\alpha^3 + \beta^3$ is

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

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If one root of the cubic equation $x^3-7x^2+36=0$ is double of another,then the number of negative roots is

If $\alpha$ and $\beta$ are roots of $x^2 - 3x + 1 = 0$,then the equation whose roots are $\frac{1}{\alpha - 2}$ and $\frac{1}{\beta - 2}$ is

Let $a, b \in \mathbb{C}$. Let $\alpha, \beta$ be the roots of the equation $x^2 + ax + b = 0$. If $\beta - \alpha = \sqrt{11}i$ and $\beta^2 - \alpha^2 = 3\sqrt{11}i$, then find the value of $|(\beta^3 - \alpha^3)^2|$.