The sum of the cubes of all the roots of the equation $x^{4}-3x^{3}-2x^{2}+3x+1=10$ is

Let $a, b$ and $c$ be positive real numbers. If $\frac{x^2-bx}{ax-c} = \frac{m-1}{m+1}$ has two roots which are numerically equal but opposite in sign,then the value of $m$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 - x - 1 = 0$,then find the equation whose roots are $\frac{1}{\beta + \gamma}, \frac{1}{\gamma + \alpha}, \frac{1}{\alpha + \beta}$.

If the roots of the equation $Ax^2 + Bx + C = 0$ are $\alpha, \beta$ and the roots of the equation $x^2 + px + q = 0$ are $\alpha^2, \beta^2$,then the value of $p$ is:

Let $p$ and $q$ be real numbers such that $p \neq 0, p^3 \neq q$ and $p^3 \neq -q$. If $\alpha$ and $\beta$ are non-zero numbers satisfying $\alpha + \beta = -p$ and $\alpha^3 + \beta^3 = q$,then find the quadratic equation whose roots are $\frac{\alpha}{\beta}$ and $\frac{\beta}{\alpha}$.

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