2. Set $A=\left\{x \mid x^{2}-3 x+2=0\right\}, C=\left\{x \mid x^{2}-m x+2=0\right\}, A \cap C=C$, then the value of the real number $m$ is
A. 3
B. 3 or $-2 \sqrt{2}<m<2 \sqrt{2}$
C. $-2 \sqrt{2}<m<2 \sqrt{2}$
D. None of the above
2. B From the problem, we know that $A=\{1,2\}$. Since $A \cap C=C$, i.e., $C \subseteq A$, $C$ can contain at most the elements 1 and 2. When $C$ contains 1 or 2, $m=3$ in both cases, at which point $A=C$; when $C=\varnothing$, the equation $x^{2}-m x+2=0$ has no real roots, then $\Delta=m^{2}-8<0$. That is, $-2 \sqrt{2}<$ $m<2 \sqrt{2}$. In summary, $m=3$ or $-2 \sqrt{2}<m<2 \sqrt{2}$.