If $\alpha, \beta$ are the roots of $ax^2+bx+c=0$,then $\left(\frac{\alpha}{a\beta+b}\right)^3 - \left(\frac{\beta}{a\alpha+b}\right)^3 = $

If $\alpha, \beta$ are the roots of $x^2 - px + q = 0$ and $\alpha', \beta'$ are the roots of $x^2 - p'x + q' = 0$,then the value of $(\alpha - \alpha')^2 + (\beta - \alpha')^2 + (\alpha - \beta')^2 + (\beta - \beta')^2$ is

Let $\alpha, \beta$ be the roots of the equation $ax^2 + 2bx + c = 0$ and $\gamma, \delta$ be the roots of the equation $px^2 + 2qx + r = 0$. If $\alpha, \beta, \gamma, \delta$ are in $G.P.$,then:

If the difference of the roots of $x^2 - px + 8 = 0$ is $2$,then the value of $p$ is

The difference between two roots of the equation $x^3-13x^2+15x+189=0$ is $2$. Then the roots of the equation are:

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - a(x + 1) - b = 0$,then $(\alpha + 1)(\beta + 1) = $