Question 79
Let $a$ and $b$ be two distinct real numbers. It is known that the two equations
$$
\begin{aligned}
& x^{2}+a x+3 b=0 \\
& x^{2}+b x+3 a=0
\end{aligned}
$$
have a common solution: what are the possible values of the sum $a+b$?
(A) 0 or -3
(B) 0 or 3
(C) Only 0
(D) Only -3
(E) There are infinitely many possible values
$$
\begin{aligned}
& x^{2}+a x+3 b=0 \\
& x^{2}+b x+3 a=0
\end{aligned}
$$
have a common solution: what are the possible values of the sum $a+b$?
(A) 0 or -3
(B) 0 or 3
(C) Only 0
(D) Only -3
(E) There are infinitely many possible values