degree 3; zeros 2,-1,-i

Question

What are the remaining zeros?

Answer 1

As Paul stated in his Comment, if -i is a zero, then its complex conjugate +i must also be a zero.  Otherwise, the coefficients will not all be real.  The minimum degree must be 4 and the zeros are

 

2

-1

-i

i

 

The polynomial is is

 

p(x) = A(x - 2)(x + 1)(x + i)(x - i)

 

with A ≠ 0.  The simplest polynomial would have A = 1.  You can expand to standard form if you wish