If $\alpha, \beta$ and $\gamma$ are roots of the equation $x^3+4x-19=0$,then the value of $\frac{\alpha^3}{19-4\alpha}+\frac{\beta^3}{19-4\beta}+\frac{\gamma^3}{19-4\gamma}$ is equal to

The value of $p$ for which the sum of the squares of the roots of the equation $x^2 - (p + 3)x + (5p - 2) = 0$ assumes its least value is:

The $G.M.$ of the roots of the equation $x^2 - 18x + 9 = 0$ is

If the roots of the equations $x^2 - bx + c = 0$ and $x^2 - cx + b = 0$ differ by the same quantity,then $b + c$ 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 $\alpha, \beta$ are the roots of $(x - a)(x - b) = c$,where $c \neq 0$,then the roots of $(x - \alpha)(x - \beta) + c = 0$ are