$2 \cdot 41$ Let the roots of the quadratic equation $x^{2}+p x+q=0$ be $p, q$, then the value of $p q$ is
(A) 0 .
(B) -2 .
(C) 0 or -2 .
(D) None of the above.
(China Shanghai Junior High School Mathematics Competition, 1985)
[Sol] From the given conditions and Vieta's formulas, we have
$$
\left\{\begin{array}{l}
p+q=-p, \\
p q=q .
\end{array}\right.
$$

From (2), we get
$q=0$ or $p=1$.

When $q=0$, from (1) we have $p=0$;
When $p=1$, from (1) we have $q=-2$.
Thus, $p q=0$ or -2.
Therefore, the answer is $(C)$.