1, -2, 3+i degree 4

Question

find a polynomial f(x) of degree 4 with real coefficients and follow the zeros. 1,-2, 3+i

Answer 1

f(x) = a(x-1)(x+2)(x-(3+i))(x-(3-i))

 

a can be any real number except 0.  The simplest polynomial is when a = 1.  Multiply it put to put it into standard form and show that the coefficients are real.