If the sum of the roots of the equation $x^2 + px + q = 0$ is three times their difference,then which one of the following is true?

If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^{2} + \lambda x - 1 = 0$ is $15$,then $6(\alpha^{3} + \beta^{3})^{2}$ is equal to

If $\alpha$ and $\beta$ are the roots of the equation $x^2-ax+b=0$,and $\alpha^2+\beta^2$ and $\alpha^3+\beta^3$ are the roots of the equation $Ax^2+Bx+C=0$,then $C=$

Let $\alpha$ and $\beta$ be the roots of the equation $p x^2 + q x + r = 0$,where $p \neq 0$. If $p, q, r$ are in $AP$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

If $\alpha, \beta \in \mathbb{R}$ are such that $1-2i$ (where $i^{2}=-1$) is a root of $z^{2}+\alpha z+\beta=0$,then $(\alpha-\beta)$ is equal to ..... .

If $\alpha, \beta$ are the roots of the equation $x^2 - px + r = 0$ and $\alpha/2, 2\beta$ are the roots of the equation $x^2 - qx + r = 0$,then what is the value of $r$?