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

lf $2 + 3i$ is one of the roots of the equation $2x^3 -9x^2 + kx- 13 = 0,$ $k \in R,$ then the real root of this equation

The number of real roots of the equation $x | x |-5| x +2|+6=0$, is

Number of rational roots of equation $x^{2016} -x^{2015} + x^{1008} + x^{1003} + 1 = 0,$ is equal to

Let $S$ be the set of all real roots of the equation, $3^{x}\left(3^{x}-1\right)+2=\left|3^{x}-1\right|+\left|3^{x}-2\right| .$ Then $\mathrm{S}$

The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is