If $\alpha, \beta, \gamma$ are the roots of the equation $x^3-4x^2-9x+36=0$ such that $\alpha+\beta=0$,then $\alpha^2+2\beta^2+3\gamma^2=$

If $\frac{1}{\sqrt{\alpha}}$ and $\frac{1}{\sqrt{\beta}}$ are the roots of the equation $ax^2 + bx + 1 = 0$ $(a \ne 0, a, b \in R)$,then the equation $x(x + b^3) + (a^3 - 3abx) = 0$ has roots

If $\alpha$ and $\beta$ are the roots of the equation $x^2-ax+b=0$,and $\alpha^2+\beta^2$ and $\alpha^3+\beta^3$ are the roots of the equation $Ax^2+Bx+C=0$,then $C=$

If $a$ and $b$ are roots of $x^2 - px + q = 0$,then $\frac{1}{a} + \frac{1}{b} = $

Let $p(x)$ be a quadratic polynomial with constant term $1$. Suppose $p(x)$, when divided by $x-1$, leaves remainder $2$ and when divided by $x+1$, leaves remainder $4$. Then, the sum of the roots of $p(x)=0$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+ax^2+bx+c=0$,then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}$ is equal to