Question

How do you write a polynomial function of least degree and leading coefficient `1` when the zeros are `4i`, `-4i`?

Answer 1

`f(x) = x^2+16`

Explanation:

If `x=a` is a zero of a polynomial, then `(x-a)` is a factor.

Hence to get the required zeros we can write:

`f(x) = (x-4i)(x+4i)`

`color(white)(f(x)) = x^2-(4i)^2`

`color(white)(f(x)) = x^2+16`

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