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

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

If $(\alpha+\sqrt{\beta})$ and $(\alpha-\sqrt{\beta})$ are the roots of the equation $x^{2}+px+q=0$,where $\alpha, \beta, p$ and $q$ are real,then the roots of the equation $(p^{2}-4q)(p^{2}x^{2}+4px)-16q=0$ are

If $\alpha^2 = 5\alpha - 3$ and $\beta^2 = 5\beta - 3$ where $\alpha \neq \beta$,what is the value of $\frac{\alpha}{\beta} + \frac{\beta}{\alpha}$?

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 $r=$

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