The solution of the equation $\frac{p + q - x}{r} + \frac{q + r - x}{p} + \frac{r + p - x}{q} + \frac{3x}{p + q + r} = 0$ is

The number of distinct real solutions for the equation $|x^2+2x-8|+x-2=0$ is

Let $p(x) = x^2 + ax + b$ have two distinct real roots,where $a, b$ are real numbers. Define $g(x) = p(x^3)$ for all real numbers $x$. Then,which of the following statements are true?
$I.$ $g$ has exactly two distinct real roots.
$II.$ $g$ can have more than two distinct real roots.
$III.$ There exists a real number $\alpha$ such that $g(x) \geq \alpha$ for all real $x$.

If the equation $x^2-3ax+a^2-2a-K=0$ has different real roots for every rational number $a$,then $K$ lies in the interval

If $-1+i$ is a root of the equation $x^4+4x^3+5x^2+2x-2=0$,then the real roots of this equation are

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 $\alpha+\beta=$