Question

How do you write a polynomial in standard form given zeros 5i and -5i?

Answer 1

`x^2+25`

Explanation:

If `color(red)(5i)` and `color(blue)(-5i)` are zeros of a polynomial
then
`color(white)("XXX")(x-color(red)(5i))` and `(xcolor(blue)(+5i))` are factors of that polynomial.

The simplest polynomial with these factors will be the product of these (and only these) factors:
`color(white)("XXX")(x-5i)(x+5i) = x^2+25`