If $\alpha, \beta, \gamma$ are the roots of $x^3+p x^2+q x+r=0$,then $\alpha^3+\beta^3+\gamma^3=$

Let $a, b, c$ be the roots of the equation $x^3 + 8x + 1 = 0$. Then the value of $\frac{bc}{(8b + 1)(8c + 1)} + \frac{ac}{(8a + 1)(8c + 1)} + \frac{ab}{(8a + 1)(8b + 1)}$ is equal to

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 $(\beta^3 - \alpha^3)^2$ is equal to:

If the roots of the equation $x^3+3px^2+3qx-8=0$ are in a geometric progression,then $\frac{q^3}{p^3}=$

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$ ($a \ne 0$; $a, b, c$ being distinct),then $(1 + \alpha + \alpha^2)(1 + \beta + \beta^2) = $

What is the sum of the squares of the roots of the equation $x^2 - 3x + 1 = 0$?