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

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 $\tan \alpha$ and $\tan \beta$ are the roots of the equation $x^2+px+q=0$,then the value of $\sin^2(\alpha+\beta)+p\cos(\alpha+\beta)\sin(\alpha+\beta)+q\cos^2(\alpha+\beta)$ is

If $\alpha, \beta, \gamma$ are the roots of the equation $2x^3+x^2-13x+6=0$,then $\alpha^3+\beta^3+\gamma^3=$

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

Which equation has roots that are the squares of the roots of the equation $ax^2 + bx + c = 0$?