Question

What is the rational zeros theorem?

Answer 1

See explanation...

Explanation:

The rational zeros theorem can be stated:

Given a polynomial in a single variable with integer coefficients:

`a_n x^n + a_(n-1) x^(n-1) + ... + a_0`

with `a_n != 0` and `a_0 != 0`, any rational zeros of that polynomial are expressible in the form `p/q` for integers `p, q` with `p` a divisor of the constant term `a_0` and `q` a divisor of the coefficient `a_n` of the leading term.

Interestingly, this also holds if we replace "integers" with the element of any integral domain. For example it works with Gaussian integers - that is numbers of the form `a+bi` where `a, b in ZZ` and `i` is the imaginary unit.