If $\alpha$ and $\beta$ are two complex roots of the equation $6 x^6-25 x^5+31 x^4-31 x^2+25 x-6=0$, then $\alpha+\beta=$

The number of integral values of $x$ satisfying $9 x-2<(x+2)^2<12 x-3$ is

If $2+\sqrt{3}$ is a root of the equation $f(x)=x^4+2 x^3-16 x^2-22 x+7=0$, then which one of the following is not a root of $f(x)=0$ ?

For $n>2$ and $n \in \mathbf{N}$, the product of the roots of $(x-n)\left(\left(x^2-2 n x\right)^2+\left(2 n^2-5\right)\left(x^2-2 n x\right)\right. \left.+\left(n^4-5 n^2+4\right)\right)=0$ is divisible by