## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$f(x)=x^4-14x^3+77x^2-200x+208$
Let us consider that $a$ is a zero of a function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$. We are given that the zeros of the function are: $3\pm2i$ and $4$ with multiplicity $2$. Therefore, we can write the equation of the function as: $f(x)=[x-(3-2i)][x-(3+2i)](x-4)(x-4)\\=(x-3-2i)(x-3+2i)(x-4)^2\\=x^4-14x^3+77x^2-200x+208$