What is the rational zeros theorem?

1 Answer
Aug 7, 2018

Answer:

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.