$2 \cdot 95$ The number of real roots of the equation $x|x|-3|x|+2=0$ is
(A) 1.
(B) 2.
(C) 3.
(D) 4.
(Tianjin City, China Junior High School Mathematics Competition, 1983;
2nd "Jinyun Cup" Junior High School Mathematics Invitational Competition, 1985)
[Solution] Consider two cases:
(1) When $x \geqslant 0$, the equation can be simplified to $x^{2}-3 x+2=0$, solving for $x$ gives
$$
x=\frac{3 \pm \sqrt{3^{2}-4 \cdot 2}}{2}=\frac{3 \pm 1}{2},
$$

both roots are valid.
(2) When $x \leqslant 0$, the equation can be simplified to $-x^{2}+3 x+2=0$, which is
$$
x^{2}-3 x-2=0 \text {. }
$$

Solving for $x$ gives $x=\frac{3 \pm \sqrt{(-3)^{2}+4 \cdot 2}}{2}=\frac{3 \pm \sqrt{17}}{2}$,
where $\frac{3+\sqrt{17}}{2}>0$ does not meet the condition.
In summary, the equation has 3 real roots.
Therefore, the correct choice is (C).