If the roots of the equation $ax^2 + bx + c = 0$ are real and of the form $\frac{\alpha}{\alpha - 1}$ and $\frac{\alpha + 1}{\alpha}$,then the value of $(a + b + c)^2$ is

Let $\alpha$ and $\beta$ be the roots of the equation $p x^2 + q x + r = 0$,where $p \neq 0$. If $p, q, r$ are in $AP$ and $\frac{1}{\alpha} + \frac{1}{\beta} = 4$,then the value of $|\alpha - \beta|$ is

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

If $\alpha_1, \alpha_2$ are the roots of $x^2+ax+1=0$ and $\alpha_3, \alpha_4$ are the roots of $x^2+bx+1=0$,then $(\alpha_1+\alpha_3)(\alpha_2+\alpha_3)(\alpha_1+\alpha_4)(\alpha_2+\alpha_4) = $

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

If $\alpha, \beta, \gamma$ and $\delta$ are zeroes of the polynomial equation $x^4-3x^2+6x-12=0$,then the value of $\frac{\alpha+\beta+\gamma}{\delta^2}+\frac{\alpha+\delta+\gamma}{\beta^2}+\frac{\alpha+\beta+\delta}{\gamma^2}+\frac{\delta+\beta+\gamma}{\alpha^2}$ is equal to