1. $a \in \mathbf{R}$, find the number of non-empty subsets of $M=|x| x \in \mathbf{R}, x^{3}+\left(a^{2}+1\right) x+2 a^{2}+10=0 \mid$.
A. 0
B. 1
C. 2
D. 7
1. $\mathrm{B}$
1. Factorize $x^{3}+\left(a^{2}+1\right) x+2 a^{2}+10=(x+2) \cdot\left(x^{2}-2 x+a^{2}+5\right)$ $\Delta=(-2)^{2}-4\left(a^{2}+5\right)<0$ Therefore, there is only 1 real root -2.