Question

Find a forth degree polynomial that has zeros 3,2,i

Answer 1

Such a polynomial could be factored as follows:
\[(x-3)(x-2)(x-i)\]
However, this is only a third degree polynomial. Your directions aren't clear if these are the only roots/zeros to the polynomial, so you could say
\[(x-3)(x-2)(x-i)(x-c)\]
where \(c\) is any number you choose.

Otherwise, you could increase the multiplicity of one of the first three roots by 1, so that you have
\[(x-3)^2(x-2)(x-i),\\(x-3)(x-2)^2(x-i),\text{ or}\\(x-3)(x-2)(x-i)^2\]