The number of roots of the equation $|x|^2 - 7|x| + 12 = 0$ is

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

If $ax^2 + bx + c = 0$,then $x =$

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 $P(x)=ax^{2}+bx+c$ and $Q(x)=-ax^{2}+dx+c$,where $ac \neq 0$ ($a, b, c, d$ are all real),then $P(x) \cdot Q(x)=0$ has

The equation whose roots are squares of the roots of $x^4-2 x^3+6 x-21=0$ is