If one root of the equation $ax^2 + bx + c = 0$ is the square of the other root,then $b^3 + a^2c + ac^2 = \dots$

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

What is the geometric mean of the roots of the equation $x^2 - 18x + 9 = 0$?

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

The minimum value of the sum of the squares of the roots of $x^{2}+(3-a)x+1=2a$ is:

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x+6=0$,then $\Sigma \alpha^2 \beta+\Sigma \alpha \beta^2$ is equal to :