The set of values of $x \in R$ satisfying the inequality $x^2 - 4x - 21 \leq 0$ is

Suppose $a, b, c$ are real numbers,and each of the equations $x^2+2ax+b^2=0$ and $x^2+2bx+c^2=0$ has two distinct real roots. Then,the equation $x^2+2cx+a^2=0$ has

If $x = 2 + 2^{2/3} + 2^{1/3},$ then $x^3 - 6x^2 + 6x = $

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:

The number of all $2$-digit numbers $n$ such that $n$ is equal to the sum of the square of the digit in its tens place and the cube of the digit in its units place is

For $n > 2$ and $n \in N$,the product of the roots of $(x-n)((x^2-2nx)^2 + (2n^2-5)(x^2-2nx) + (n^4-5n^2+4)) = 0$ is divisible by