MathNet 2021 — Part 02 Question 76

Suppose the domain of function $f(x)$ is $D = (-\infty, 0) \cup (0, +\infty)$ and there is $f(x) = \frac{f(1) \cdot x^2 + f(2) \cdot x - 1}{x}$ for any $x \in D$. Then the sum of all the zeros of $f(x)$ is ______.