Let $r$ be a real number and $n \in N$ be such that the polynomial $2 x^2+2 x+1$ divides the polynomial $(x+1)^n-r$. Then, $(n, r)$ can be
$\left(4000,4^{1000}\right)$
$\left(4000, \frac{1}{4^{1000}}\right)$
$\left(4^{1000}, \frac{1}{4^{1000}}\right)$
$\left(4000, \frac{1}{4000}\right)$
If two roots of the equation ${x^3} - 3x + 2 = 0$ are same, then the roots will be
If $|{x^2} - x - 6| = x + 2$, then the values of $x$ are
If $2 + i$ is a root of the equation ${x^3} - 5{x^2} + 9x - 5 = 0$, then the other roots are
The sum of all the roots of the equation $\left|x^2-8 x+15\right|-2 x+7=0$ is: