Answer
$x^4-6x^3+17x^2-28x+20$
Work Step by Step
Step 1. Given zeros $x=1+2i$ and $x=2$ (multiplicity 2), we can identify one more zeros as $x=1-2i$
Step 2. We can write the polynomial as $f(x)=(x-2)^2(x-1-2i)(x-1+2i)=(x^2-4x+4)((x-1)^2-(2i)^2)=(x^2-4x+4)(x^2-2x+5)$
Step 3. Continue from above, we have $f(x)=x^4-6x^3+17x^2-28x+20$
