Question

If a polynomial has integral coefficients with the following roots, then what other roots must it have?
3 + i
1 + radical3
Select all that apply

3 – i

–3 – i

-1 + raical3

-1- raical3

no other roots

Answer 1

Select: 3 – i

Reason: integer coefficients are real, so nonreal roots come in complex-conjugate pairs. Thus 3+i implies 3−i is a root. The conjugate of 1+√3 is 1−√3, which is not among the choices (−1±√3 are different), so none of those are required.