If the roots of the equation $(b - c)x^2 + (c - a)x + (a - b) = 0$ are equal,then $a, b, c$ are in which progression?

Let $\alpha, \alpha^2$ be the roots of $x^2 + x + 1 = 0$. Then the equation whose roots are $\alpha^{31}, \alpha^{62}$ is:

If the roots of the equation $3x^2 + 4kx + 3 = 0$ are non-real,then $k$ lies in the interval

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is:

The product of the real roots of the equation $(x+1)^4+(x+3)^4=8$ is

If $a, b, c \in Q$,then the roots of the equation $(b + c - 2a)x^2 + (c + a - 2b)x + (a + b - 2c) = 0$ are