Question

How do you write a polynomial equation of least degree given the roots -1, 1, 3, -3?

Answer 1

`x^4-10x^2+9 = 0`

Explanation:

A polynomial in `x` has a zero `a` if and only if it has a factor `(x-a)`.

So a polynomial in `x` with zeros `-1`, `1`, `3` and `-3` must be a multiple of:

`(x+1)(x-1)(x-3)(x+3) = (x^2-1)(x^2-9) = x^4-10x^2+9`

So a polynomial equation of minimum degree with roots `-1`, `1`, `3` and `-3` is:

`x^4-10x^2+9 = 0`