1. Given $a$ is a real number. Then, the number of subsets of the set $M=|x| x^{2}-3 x-a^{2}+2=0, x \in$ $\mathbf{R}$ : is ( ).
A. 1
B. 2
C. 4
J). Uncertain
1. $\mathrm{C}$

From the discriminant $\Delta=1+4 a^{2}>0$ of the equation $x^{2}-3 x-a^{2}+2=0$, we know that the equation has two distinct real roots. Therefore, $M$ has 2 elements, and the set $M$ has $2^{2}=4$ subsets.