3. Let $[x]$ denote the greatest integer not exceeding the real number $x$. Then the equation $x^{2}-[x]-2=0$ has $(\quad)$ distinct real roots.
(A) 1
(B) 2
(C) 3
(D) 4
3. C.
$$
\begin{array}{l}
\text { Given }[x] \leqslant x, x^{2}-[x]-2=0 \\
\Rightarrow x^{2}-x-2 \leqslant 0 \Rightarrow x \in[-1,2] \\
\Rightarrow[x] \text { can only be }-1, 0, 1, 2 \\
\Rightarrow x=-1, \sqrt{3}, 2 .
\end{array}
$$