Answer
$f(x)=x^4-14x^3+77x^2-200x+208.$
Work Step by Step
If $a$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “multiplier” of the function.
The given zeros of the function are: $3\pm2i$ and $4$ with multiplicity $2$.
Hence the function could e.g. be: $a(x-(3-2i))(x-(3+2i))(x-4)(x-4)\\=a(x-3-2i)(x-3+2i)(x-4)^2\\=a(x^4-14x^3+77x^2-200x+208).$
If $a=1$, the function is $f(x)=x^4-14x^3+77x^2-200x+208.$
(The degree is $4$ which is good).
