What is the rational zeros theorem?

1 Answer
Aug 7, 2018

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.