Question

How do you write a polynomial equation of least degree given the roots -5i, -i, i, 5i?

Answer 1

`x^4+26x^2+25 = 0`

Explanation:

Each zero `a` corresponds to a factor `(x-a)`.

So we can write:

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

`color(white)(f(x)) = (x^2+25)(x^2+1)`

`color(white)(f(x)) = x^4+26x^2+25`

So a suitable polynomial equation is:

`x^4+26x^2+25 = 0`