If $\alpha$ is a multiple root of the equation $x^5-6x^4+11x^3-2x^2-12x+8=0$,then $3\alpha^2-2\alpha+1=$

Let $p, q$ and $r$ be real numbers $(p \ne q, r \ne 0)$ such that the roots of the equation $\frac{1}{x + p} + \frac{1}{x + q} = \frac{1}{r}$ are equal in magnitude but opposite in sign. Then the sum of squares of these roots is equal to:

If the quadratic equation $3x^2 + (2k + 1)x - 5k = 0$ has real and equal roots,then the value of $k$ such that $-\frac{1}{2} < k < 0$ is

The sum of the non-real roots of $(p^2+p-3)(p^2+p-2)-12=0$ is

If the set of all $a \in R - \{1\}$,for which the roots of the equation $(1-a)x^2 + 2(a-3)x + 9 = 0$ are positive,is $(-\infty, -\alpha] \cup [\beta, \gamma)$,then $2\alpha + \beta + \gamma$ is equal to . . . . . . .

If $x^2 - 3x + 2$ is a factor of $x^4 - px^2 + q$,then $(p, q) = $