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 $\alpha+\beta=$

Let $r(x)$ be the remainder when the polynomial $x^{135}+x^{125}-x^{115}+x^5+1$ is divided by $x^3-x$. Then,

When $b=17$,it is found that the roots of the equation $x^2+bx+c=0$ are $-2$ and $-15$. If $\alpha, \beta$ are the roots of the same equation when $b=13$,then $|\alpha-\beta|=$

If $\alpha$ and $\beta$ are the roots of $x^2+3(a+3)x-9a=0$ such that the roots are equal for different values of $a$ (where $\alpha > \beta$ is not applicable as roots are equal,but let $\alpha$ be the root for $a=-9$ and $\beta$ be the root for $a=-1$),then the minimum value of the expression $x^2+\alpha x-\beta$ is:

The minimum value of $(x-\alpha)(x-\beta)$ is

What are the real roots of the equation $x^2 + 5|x| + 4 = 0$?