1. Given that $a$ is a given real number, 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
(C)
I. Multiple Choice Question
1.【Analysis and Solution】 $M$ represents the solution set of the equation $x^{2}-3 x-a^{2}+2=0$ in the real number range. Since $\Delta=1+4 a^{2}>$ 0, $M$ contains 2 elements. Therefore, the set $M$ has $2^{2}=4$ subsets, choose C.