The roots of the equation $a(x^2 + 1) - (a^2 + 1)x = 0$ are

If the equation $x^4 - 4x^3 + ax^2 + bx + 1 = 0$ has four real roots $\alpha, \beta, \gamma, \delta$,then the values of $a$ and $b$ are:

The equation $x^2-4x+[x]+3=x[x]$,where $[x]$ denotes the greatest integer function,has:

Let $S = \{x^{3} + ax^{2} + bx + c : a, b, c \in \mathbb{N} \text{ and } a, b, c \le 20\}$ be a set of polynomials. Then the number of polynomials in $S$,which are divisible by $x^{2} + 2$,is

What is the remainder of $2x^3 - 5x^2 + 7$ when divided by $(x - 2)$?

Solve the equation $-x^{2}+x-2=0$.