Answer
$x=2$ (multiplicity 2).
$f(x) =(x-2)^2(x^2+5)$.
Work Step by Step
Step 1. List possible rational zeros $\frac{p}{q}:\pm1,\pm2,\pm4,\pm5,\pm10,\pm20$.
Step 2. Use synthetic division as shown to find zero(s) $x=2$ (multiplicity 2).
Step 3. Use the quotient to find other zero(s) $x^2+5=0$, no real solutions.
Step 4. Thus $f(x)=x^4-4x^3+9x^2-20x+20=(x-2)^2(x^2+5)$.
