If $k \in (-\infty, -2) \cup (2, \infty)$,then the roots of the equation $x^2 + 2kx + 4 = 0$ are

If $f(x)$ is a second degree polynomial such that $f(x) \geq 0$ for all $x \in R$,$f(-3) = 0$,and $f(0) = 18$,then find $f(3)$.

Let $[x]$ denote the greatest integer less than or equal to $x$. Then,the values of $x \in \mathbb{R}$ satisfying the equation $[e^{x}]^{2} + [e^{x} + 1] - 3 = 0$ lie in the interval:

If $\alpha$ and $\beta$ are the least positive integers such that for all $n \in N$, $n^3+\alpha n$ is divisible by $3$ and $n^3-\beta n$ is divisible by $6$, then $\alpha+\beta=$

Sum of the solutions of the equation $[x^2] - 2x + 1 = 0$ is (where $[.]$ denotes the greatest integer function).

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is: