If $\alpha, \beta$ are the roots of $x^2 - x + p = 0$ and $\gamma, \delta$ are the roots of $x^2 - 4x + q = 0$,and if $\alpha, \beta, \gamma, \delta$ are in a geometric progression,then the values of $p$ and $q$ are respectively:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 1 = 0$,the value of $\alpha^3 + \beta^3$ is:

If $\alpha$ and $\beta$ are roots of the equation $x^2 - 4\sqrt{2}kx + 2e^{4\ln k} - 1 = 0$ for some $k$,and $\alpha^2 + \beta^2 = 66$,then $\alpha^3 + \beta^3$ is equal to: (in $\sqrt{2}$)

If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+3x^3-6x^2+2x-4=0$,then find the equation having roots $\frac{1}{\alpha}, \frac{1}{\beta}, \frac{1}{\gamma}$ and $\frac{1}{\delta}$.

If $\alpha$ and $\beta$ are roots of $ax^{2}+bx+c=0$, then the equation whose roots are $\alpha^{2}$ and $\beta^{2}$ is

The roots of the quadratic equation $3x^2 - px + q = 0$ are the $10^{\text{th}}$ and $11^{\text{th}}$ terms of an arithmetic progression with a common difference $d = \frac{3}{2}$. If the sum of the first $11$ terms of this arithmetic progression is $88$,then $q - 2p$ is equal to: