Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. 3, 1+2i

Answer 1

P(x) = (x - 3)(x - (1 + 2i))(x - (1 - 2i))

P(x) = (x - 3)(x - 1 - 2i)(x - 1 + 2i)

P

Answer 2

1 + 2i = x

x-1=2i

square both sides

x^2-2x + 1 = -4

simplify

x^2 -2x+5 is one factor

another is x-3

(x-3)(x^2-2x+5) = x^3-5x^2+11x -15 is the least degree polynomial with leading coefficient 1 and the given 2 zeros. There's necessarily a 3rd zero as irrational zeros come in conjugate paris.