If $\alpha, \beta, \gamma$ are the roots of $x^3+2x+5=0$,then $\sum \frac{\beta+\gamma}{\alpha^2} = $

If $p$ and $q$ are the roots of the equation $x^{2}+px+q=0$,then:

If $a$ and $b$ are the roots of the equation $y^2+y+1=0$,then the value of $a^4+b^4+a^{-1}b^{-1}$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-6x^2+11x-6=0$ and if $a=\alpha^2+\beta^2+\gamma^2$,$b=\alpha\beta+\beta\gamma+\gamma\alpha$ and $c=(\alpha+\beta)(\beta+\gamma)(\gamma+\alpha)$,then the correct inequality among the following is

The quadratic equation whose sum of the roots is $11$ and sum of squares of the roots is $61$ is

Let $\alpha, \beta, \gamma$ be the roots of $x^3+x+10=0$ and $\alpha_1=\frac{\alpha+\beta}{\gamma^2}, \beta_1=\frac{\beta+\gamma}{\alpha^2}, \gamma_1=\frac{\gamma+\alpha}{\beta^2}$. Then,the value of $(\alpha_1^3+\beta_1^3+\gamma_1^3)-\frac{1}{10}(\alpha_1^2+\beta_1^2+\gamma_1^2)$ is