If the product of roots of the equation $mx^2 + 6x + (2m - 1) = 0$ is $-1$,then the value of $m$ will be

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + 6x + \lambda = 0$ and $3\alpha + 2\beta = -20$,then $\lambda = $

If $\alpha$ and $\beta$,$\alpha$ and $\gamma$,$\alpha$ and $\delta$ are the roots of the equations $ax^2 + 2bx + c = 0$,$2bx^2 + cx + a = 0$ and $cx^2 + ax + 2b = 0$ respectively,where $a, b$ and $c$ are positive real numbers,then $\alpha + \alpha^2 = $

$\alpha$ and $\beta$ are the roots of $x^2+2x+c=0$. If $\alpha^3+\beta^3=4$,then the value of $c$ is

If the roots of the equation $x^3+3px^2+3qx-8=0$ are in a geometric progression,then $\frac{q^3}{p^3}=$

$\alpha, \beta, \gamma$ are the roots of the equation $8x^3 - 42x^2 + 63x - 27 = 0$. If $\beta < \gamma < \alpha$ and $\beta, \gamma, \alpha$ are in geometric progression,then the extreme value of the expression $\gamma x^2 + 4\beta x + \alpha$ is