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

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

If $\alpha+\beta=-2$ and $\alpha^3+\beta^3=-56$,then the quadratic equation whose roots are $\alpha$ and $\beta$ is

$\alpha, \beta, \gamma$ 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

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 + 2(a + b)x + a^2 + b^2 = 0$,then the equation whose roots are $(\alpha + \beta)^2$ and $(\alpha - \beta)^2$ is

If the ratio of the roots of the equation $12x^2 - mx + 5 = 0$ is $2 : 3$,then $m = .....$