Answer
$\{4,\pm5i \}$
Work Step by Step
Step 1. Given $f(x)=x^3-4x^2+25x-100$, list the potential rational zeros as $\pm1,\pm2,\pm4,\pm5,\pm10,\pm20,\pm25,\pm50,\pm100$.
Step 2. Use synthetic division to find a real zeros $x=4$ as shown in the figure.
Step 3. Use the quotient and solve $x^2+25=0$ to get $x=\pm5i$
Step 4. Thus the zeros are $\{4,\pm5i \}$
