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
$-1 .(\mathrm{C})$
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.