If $\alpha, \beta, \gamma$ are the roots of the equation $5x^3 - 3x^2 + 2x - 4 = 0$,then find the value of $\sum \alpha^2 \beta^2$.

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+4x+1=0$,then $(\alpha+\beta)^{-1}+(\beta+\gamma)^{-1}+(\gamma+\alpha)^{-1}$ is equal to

If $\alpha$ and $\beta$ are two roots of the equation $x^{2}-64x+256=0$,then the value of $\left(\frac{\alpha^{3}}{\beta^{5}}\right)^{\frac{1}{8}}+\left(\frac{\beta^{3}}{\alpha^{5}}\right)^{\frac{1}{8}}$ is

If in the equation $ax^2 + bx + c = 0$,the sum of roots is equal to the sum of the squares of their reciprocals,then $\frac{c}{a}, \frac{a}{b}, \frac{b}{c}$ are in

If $\sin \alpha$ and $\cos \alpha$ are the roots of the equation $ax^2 + bx + c = 0$ $(c \neq 0)$,then:

If $\alpha$ and $\beta$ are the roots of the equation $a x^2+b x+c=0$ and if $p x^2+q x+r=0$ has roots $\frac{1-\alpha}{\alpha}$ and $\frac{1-\beta}{\beta}$,then $r$ is equal to