If $\alpha, \beta, \gamma$ are the roots of $x^3+p x^2+q x+r=0$,then the value of $(1+\alpha^2)(1+\beta^2)(1+\gamma^2)$ is

The condition that the roots of $x^3-b x^2+c x-d=0$ are in geometric progression is

If $\frac{\alpha}{\alpha+1}$ and $\frac{\beta}{\beta+1}$ are the roots of the quadratic equation $x^2+7x+3=0$,then the equation having roots $\alpha$ and $\beta$ is

If the ratio of the roots of the equation $px^2+qx+r=0$ is $a:b$,then $\frac{ab}{(a+b)^2}=$

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $x^3-3x^2+x+5=0$,then $y=\Sigma \alpha^2+\alpha \beta \gamma$ satisfies the equation

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 = $