Question

Suppose you know that a 3rd degree polynomial has 6 and 3-i as two of its zeros

What other zeros does the polynomial have?

Answer 1

that will be complex conjugate of 3 - i, hence 3 + i

Answer 2

This assumes that the polynomial does not have any complex coefficient

Answer 3

Complex solutions come in pairs - there is a theorem that states that
if you know one of the solutions is 3-i you can assume 3+i is the other solution.