$2 \cdot 96$ The number of real roots of the equation $x|x|-3|x|-4=0$ is
(A) 1 .
(B) 2 .
(C) 3 .
(D) 4 .
(2nd China Tianjin "Chinese Youth Cup" Mathematics Invitational, 1987)
[Solution] When $x \geqslant 0$, the equation can be transformed into $x^{2}-3 x-4=0$, solving which yields $x=4$ or -1 (which does not meet the initial condition, so it is discarded).

When $x<0$, the equation can be transformed into $-x^{2}+3 x-4=0$, i.e.,
$$
x^{2}-3 x+4=0 \text {. }
$$

Since its discriminant $\Delta=3^{2}-4 \cdot 4<0$, there are no real roots.
In summary, the equation has only one real root.
Therefore, the answer is $(A)$.