If the roots of the equation $(x - a)(x - b) = c$ (where $c \neq 0$) are $\alpha$ and $\beta$,then what are the roots of the equation $(x - \alpha)(x - \beta) + c = 0$?

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3 - x - 1 = 0$,then what is the value of $\left( \frac{1 + \alpha}{1 - \alpha} \right) \left( \frac{1 + \beta}{1 - \beta} \right) \left( \frac{1 + \gamma}{1 - \gamma} \right)$?

If the sum of the roots of the equation $ax^2 + bx + c = 0$ is equal to the sum of the squares of their roots,then:

If $\alpha, \beta, \gamma$ are roots of the equation $x^3+a x^2+b x+c=0$,then $\alpha^{-1}+\beta^{-1}+\gamma^{-1} = $

If $p$ and $q$ are the roots of the equation $x^2 + pq = (p + 1)x$,then $q=$

If the roots of the equation $12x^2 - mx + 5 = 0$ are in the ratio $2 : 3$,then $m =$