3. (2001 National High School Competition Question) Given that $a$ is a given 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
3. Choose C. Reason: From the discriminant of the equation $x^{2}-3 x-a^{2}+2=0$, $\Delta=1+4 a^{2}>0$, we know that the equation has two distinct real roots, so $M$ has 2 elements, thus the set $M$ has $2^{2}=4$ subsets.