Question

What is a polynomial function for 5, i, -i?

Answer 1

`f(x)=x^3-5x^2+x-5`

Explanation:

I have assumed that `{5,i,-i}` are intended to be the zeros of the function.

In this case, the function can be factored as:
`color(white)("XXX")(x-5)((x-i)(x+i)`

`color(white)("XXX")=(x-5)(x^2-i^2)`

`color(white)("XXX")=(x-5)(x^2+1)`

`color(white)("XXX")=x^3+x -5x^x-5`

(or in standard polynomial form)
`color(white)("XXX")=x^3-5x^2+x-5`