If $\alpha, \beta, \gamma$ are roots of $x^3-5x+4=0$,then $(\alpha^3+\beta^3+\gamma^3)^2$ is equal to

Let $\alpha, \beta$ be the roots of the equation $x^{2}-6x-2=0$ with $\alpha>\beta$. If $a_{n}=\alpha^{n}-\beta^{n}$ for $n \geq 1$, then the value of $\frac{a_{10}-2a_{8}}{2a_{9}}$ is

The value of $k$ for which one of the roots of ${x^2} - x + 3k = 0$ is double of one of the roots of ${x^2} - x + k = 0$ is

If $\alpha, \beta$ are the roots of $x^2+p x+q=0$,then the values of $\alpha^3+\beta^3$ and $\alpha^4+\alpha^2 \beta^2+\beta^4$ are respectively ...... and ......

If one root of the equation $4x^2 - 2x + k - 4 = 0$ is the reciprocal of the other,then the value of $k$ is

If $\alpha, \beta$ and $\gamma$ are roots of $x^{3}-2x+1=0$,then the value of $\sum\left(\frac{1}{\alpha+\beta-\gamma}\right)$ is