Explain why the following is a contradictory statement, f(x) is a polynomial function of degree 3 whose coefficients are real numbers its zeros are 2, i and 3+i

Question

Explain why the following is a contradictory statement, f(x) is a polynomial function  of degree 3 whose coefficients are real numbers its zeros are 2, i and 3+i

perl · Answer

because complex roots come in 'conjugate' pairs , so you have zeroes
2, i, -i, 3 + i, 3 - i

perl · Answer

the minimum degree of a polynomial with real coefficients with zeroes 2, i, 3+i is 5

perl · Answer

in general, if f(x) is a polynomial and  f(a+bi) = 0 ,  then f(a - bi) = 0