Question 135278
Two things:

First, if a polynomial equation has a complex number root ({{{a+bi}}}), then it also has the conjugate of that complex number as a root ({{{a-bi}}}).  That means that, although you were only given three numbers as roots, there are actually four, namely:

{{{3}}}, {{{-9}}}, {{{3+2i}}}, and {{{3-2i}}}


Second, a polynomial equation has a root {{{a}}} if and only if {{{(x-a)}}} is a factor of the polynomial.


So if the desired polynomial is {{{P(x)}}}, then {{{P(x)=(x-3)(x+9)(x-(3+2i))(x-(3-2i))}}}.  All you need to do now is multiply the factors and collect like terms.  Hint: Remember when you are working it out that {{{i^2=-1}}}, so {{{2i(-2i)=4}}} not {{{-4}}}.