2. Given that $a$ is a non-negative integer, if the equation $2 x-a \sqrt{1-x}-a+4=0$ has at least one integer root. Then the number of possible values for $a$ is ( ).
(A) 1
(i) 2
(C) 3
(D) 4
2. (C).

From the meaningful radicand, we know $x \leqslant 1$.
Also, $2 x+4=a(\sqrt{1-x}+1) \geqslant 0$,
so $x \geqslant-2$.
When $x=1,0,-2$, $a$ takes the values $6,2,0$ respectively.
When $x=-1$, $a$ is not an integer.
Therefore, $a$ has a total of 3 possible values.