3. Given the function
$y=\left(k^{2}+k\right) x^{2}-\sqrt{5}(k+1) x+1(k$ is a constant $)$, the graph of the function intersects the coordinate axes at two points. Which of the following conclusions is correct? ( ).
(A) $k=-5$
(B) $k=-1$ or -5
(C) $k=0$ or -5
(D) $k-1$
3. C.

From the problem, we know that the given function is either a linear function or a quadratic function that intersects the $x$-axis at one point. Therefore,
$$
\left\{\begin{array}{l}
k^{2}+k=0, \\
-\sqrt{5}(k+1) \neq 0
\end{array}\right.
$$

or $\left\{\begin{array}{l}k^{2}+k \neq 0, \\ \Delta=5(k+1)^{2}-4\left(k^{2}+k\right)=0 .\end{array}\right.$
Solving, we get $k=0$ or $k=-5$.