There are many polynomials that fit the bill, f(x)=a(x-r1)(x-r2)(x-r3)(x-r4) where a is any real number not equal to zero. A simple one is when a=1. where r1,r2,r3,r4 are the roots of the 4th degree polynomial. Also note that for a polynomial with *real* coefficients, complex roots *always* come in conjugages, i.e. in the form a±bi [±=+/-]
So a polynomial would be: f(x)=(x-(-4-5i))(x-(-4+5i))(x--2)(x--2) or, simplifying f(x)=(x+4+5i)(x+4-5i)(x+2)^2 =x^4+12x^3+77x^2+196x+164 [if you decide to expand]
