Answer:
[tex]f(x)=x^3-2x^2+9x-18[/tex]
Explanation:
If the zeroes of the polynomial function are: 2, 3i, and -3i.
We have that:
[tex]x=2,x=3i,x=-3i[/tex]
This implies that:
[tex]\begin{gathered} x-2=0\text{ or }x-3i=0\text{ or }x+3i=0 \\ \implies(x-2)(x-3i)(x+3i)=0 \end{gathered}[/tex]
We multiply the factors
[tex]\begin{gathered} (x-2)(x^2-9i^2)=0 \\ (x-2)(x^2+9)=0 \\ x^3+9x-2x^2-18=0 \\ x^3-2x^2+9x-18=0 \end{gathered}[/tex]
The polynomial function therefore is:
[tex]f(x)=x^3-2x^2+9x-18[/tex]
