Write a polynomial function f(x) of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros: 0,1, and 3i

Answer 1

(x-0)(x-1)(x-3i)(x+3i) =

x(x-1)(x^2+9) =

x(x^3 -x^2 +9x -9) =

x^4 -x^3 + 9x^2 -9x

f(x) = x^4 -x^3 + 9x^2 -9x