If $r$ and $s$ are positive,what is the nature of the roots of the quadratic equation $ax^2 - rx - s = 0$?

If $x = 2 + 2^{2/3} + 2^{1/3},$ then $x^3 - 6x^2 + 6x = $

The sum of all the real values of $x$ satisfying the equation $2^{(x - 1)(x^2 + 5x - 50)} = 1$ is

If $\frac{1+\sqrt{3}i}{2}$ is a root of the equation $x^4-x^2+x-1=0$,then its real roots are:

If $3 + 4i$ is a root of the equation ${x^2} + px + q = 0$ where $p$ and $q$ are real numbers,then:

If roots of the equation $ax^2 + bx + c = 0$ are $(\alpha - \beta)$ and $(\gamma - \delta)$,and roots of the equation $Ax^2 + Bx + C = 0$ are $(\alpha + \delta)$ and $(\beta + \gamma)$,then $\left| \frac{a}{A} \right|$ is equal to (where $D_1$ and $D_2$ are discriminants of the given equations respectively).