Question

How do you write a polynomial in standard form given the zeros x=5, 8i, and -8i?

Answer 1

`f(x) = x^3-5x^2+64x-320`

Explanation:

We find the simplest such polynomial by multiplying the corresponding linear factors:

`f(x) = (x-5)(x-8i)(x+8i)`

`color(white)(f(x)) = (x-5)(x^2-(8i)^2)`

`color(white)(f(x)) = (x-5)(x^2+64)`

`color(white)(f(x)) = x^3-5x^2+64x-320`

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