Question

How do you write a polynomial function of least degree with integral coefficients that has the given zeroes 6, 2i?

Answer 1

`f(x) = x^3-6x^2+4x-24`

Explanation:

If a polynomial has Real coefficients then any non-Real zeros will occur in Complex conjugate pairs. So if `2i` is a zero, then so is `-2i`.

Hence our polynomial function can be written:

`f(x) = (x-6)(x-2i)(x+2i)`

`= (x-6)(x^2+4)`

`= x^3-6x^2+4x-24`

Any polynomial in `x` with these zeros will be a multiple (scalar or polynomial) of this `f(x)`