2. If the positive root of the quadratic equation $x^{2}-p x-q=0$ $\left(p, q \in \mathbf{N}_{+}\right)$ is less than 3, then the number of such quadratic equations is ( ).
(A) 5
(B) 6
(C) 7
(D) 8
2.C.

From $\Delta=p^{2}+4 q>0,-q<0$, 
it follows that $3 p+q<9$.
Given $p, q \in \mathbf{N}_{+}$, then $p=1, q \leqslant 5$ or $p=2, q \leqslant 2$.
Therefore, there are 7 pairs $(p, q)$ that satisfy the conditions.