Question

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros 2, 2i, and 4-sqrt 6

Answer 1

f(x) = (x-2)(x-2i)(x+2i)(x-4+√6)

Answer 2

If you want rational coefficients, then that √6 has to go, just like the i terms. So, you need

f(x) = (x-2)(x-2i)(x+2i)(x-(4-√6))(x-(4+√6))
= (x-2)(x^2+4)((x-4)+√6)((x-4)-√6)
= (x-2)(x^2+4)(x^2-8x+10)