Third degree polynomial functions

Question

Form a third degree polynomial function with real coefficients such that -6+i and -1are zeros

Answer 1

x= -6+i is one zero

x+6 = i square both sides to remove the imaginary term

(x+6)^2 = -1 which adds another zero the conjugate: x=-6-i, that makes the coefficients all real

x^2 + 18x + 36 + 1 = 0

(x+1)(x^2 + 18x + 37) =0

x^3 + 19x^2 55x + 37 has 3 zeroes, all real

Answer 2

P(x) = (x + 1)(x - (-6 +i))(x - (-6 - i))