If 2i is a zero then -2i is also a zero. (x-2i)(x+2i)=x2+4 is a factor.
If √3 is a zero then -√3 is another zero if polynomial has rational coefficients. (x-√3)(x+√3)=x2-3 is a factor.
x-4 is also a factor.
Polynomial could be (x2+4)(x2-3)(x-4)=
(x4+x2-12)(x-4)=
x5-4x4+x3-4x2-12x+48.