Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros. −1, 2, 4i

Answer 1

I would start with the factored form of the polynomial using the given zeros:

f(x) = (x+1)(x-2)(x^2+16)

Note that we have to use x^2+16 rather than x-4i because the coefficients must be rational. Multiplying this out, we get:

f(x) = x^4-x^3+14x^2-16x-32