Let $a$ and $b$ be positive real numbers. The equations
$$\begin{aligned}
& x^{2} + ax + b = 0 \\
& ax^{2} + (b + 3)x + a = 0
\end{aligned}$$
are given.
Given that the solution set of each of these equations has exactly 1 element, what is the product of the different values that the sum $a + b$ can take?
A) 24
B) 32
C) 45
D) 72
E) 120