1. Given $a$ is a real number. Then the number of subsets of the set $M=\left\{x \mid x^{2}-3 x-a^{2}+2=0, x \in \mathbf{R}\right\}$ is
A. 1
B. 2
C. 4
D. Uncertain
Solve:
$\Delta=9+4\left(a^{2}-2\right)=4 a^{2}+1>0$, then the equation $x^{2}-3 x-a^{2}+2=0$ has 2 distinct real roots, and the number of subsets of set $A$ is 4. Therefore, the answer is $C$.