For the equation $\frac{1}{x + a} - \frac{1}{x + b} = \frac{1}{x + c}$,if the product of the roots is zero,what is the sum of the roots?

For what value of $a$ is the difference of the roots of the equation $2x^2 - (a + 1)x + (a - 1) = 0$ equal to their product?

If $\alpha$ and $\beta$ are the roots of the equation $2x^2 + 6x + k = 0$,then the maximum value of $\left[\frac{\alpha}{\beta} + \frac{\beta}{\alpha}\right]$ when $k < 0$ is (where $[\cdot]$ denotes the greatest integer function)

If $8$ and $2$ are the roots of ${x^2} + ax + \beta = 0$ and $3$ and $3$ are the roots of ${x^2} + \alpha x + b = 0$,then the roots of ${x^2} + ax + b = 0$ are

Let $\alpha$ and $\beta$ be the roots of the quadratic equation $ax^2 + bx + c = 0$. If $a, b, c$ are in $A.P.$ and $\alpha + \beta = 15$,then $\alpha \beta$ equals:

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