2.50 If $c$ is a real number, and the opposite of a solution of $x^{2}-3 x+c=0$ is a solution of $x^{2}+3 x-c=0$, then the solutions of $x^{2}-3 x+c=0$ are
(A) 1,2.
(B) $-1,-2$.
(C) 0,3.
(D) $0,-3$.
(E) $\frac{3}{2}, \frac{3}{2}$.
(27th American High School Mathematics Examination, 1976)
[Solution] Let $r$ be a solution of $x^{2}-3 x+c=0$, then $-r$ is a solution of $x^{2}+3 x-$ $c=0$, thus
$$
r^{2}-3 r+c=0, \quad r^{2}-3 r-c=0 .
$$

Solving these equations yields $c=0$. Therefore, the solutions of $x^{2}-3 x+c=0$ are 0 and 3. Hence, the correct choice is $(C)$.