Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. Write the function in standard form

Question

3,1+2i

Answer 1

x= 1+2i

x-1 = 2i

x^2 -2x + 1= -4

x^2 -2x +5 = 0

f(x) = (x-3)(x^2 -2x +5)

f(x) = x^3 -5x^2 +11x -15