2. Given that $a$ is a natural number, the equation with respect to $x$
$$
2 x-a \sqrt{1-x}-a+4=0
$$

has at least one integer root. Then the number of possible values for $a$ is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
2.C.

Obviously, $x \leqslant 1$.
Also, $2 x+4=a(\sqrt{1-x}+1) \geqslant 0$, so $x \geqslant-2$. When $x=1,0,-2$, $a$ is $6,2,0$ respectively; when $x=-1$, $a$ is not an integer. Therefore, there are 3 possible values for $a$.