If $\alpha, \beta, \gamma$ are the roots of $2x^3 - 2x - 1 = 0$,then $(\Sigma \alpha \beta)^2$ is equal to

If the sum of two roots of the equation $x^4-2x^3+x^2+4x-6=0$ is zero,then the sum of the squares of the other two roots is

If $\alpha$ and $\beta$ are the roots of the equation $ax^2 + bx + c = 0$,then $\frac{\alpha}{a\beta + b} + \frac{\beta}{a\alpha + b} = $

The value of $k$ for which one of the roots of ${x^2} - x + 3k = 0$ is double of one of the roots of ${x^2} - x + k = 0$ is

If the roots of the given equation $(2k + 1)x^2 - (7k + 3)x + k + 2 = 0$ are reciprocal to each other,then the value of $k$ will be

If $\alpha, \beta$ are the roots of $ax^2 + bx + c = 0$ and $\gamma, \delta$ are the roots of $px^2 + qx + r = 0$,and $D_1, D_2$ are their respective discriminants. If $\alpha, \beta, \gamma, \delta$ are in arithmetic progression,then $D_1 : D_2 = \dots$