If $\alpha$ and $\beta$ are the roots of the equation $x^2-4x+5=0$,then the quadratic equation whose roots are $\alpha^2+\beta$ and $\alpha+\beta^2$ 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:

If $p$ and $q$ are the roots of the equation $x^2 + pq = (p + 1)x$,then $q=$

If $\alpha, \beta$ and $\gamma$ are the roots of ${x^3} + px + q = 0$,then the value of ${\alpha^3} + {\beta^3} + {\gamma^3}$ is equal to

If $\alpha_1, \alpha_2, \alpha_3, \alpha_4, \alpha_5$ are the roots of $x^5-5 x^4+9 x^3-9 x^2+5 x-1=0$,then $\frac{1}{\alpha_1^2}+\frac{1}{\alpha_2^2}+\frac{1}{\alpha_3^2}+\frac{1}{\alpha_4^2}+\frac{1}{\alpha_5^2}=$

If $\alpha$ and $\beta$ are the roots of the equation $ax^2+bx+c=0$,then the equation whose roots are $\alpha+\beta$ and $\frac{1}{\alpha}+\frac{1}{\beta}$ is