Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Rational roots

  1. Feb 14, 2007 #1
    can a non-factorable function has rational real roots?
     
    Last edited: Feb 14, 2007
  2. jcsd
  3. Feb 14, 2007 #2

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Yes, for example take [itex]f(x):= x+a[/itex] where [itex]a \in \mathbb{Q}[/itex].
     
  4. Feb 14, 2007 #3

    StatusX

    User Avatar
    Homework Helper

    Are you asking if a polynomial with rational coefficients which cannot be written as the product of polynomials with rational coefficients of smaller degree can have rational roots? Except for the trivial case of polynomials of degree one, the answer is no, because any rational root a of f(x) translates to a linear factor (x-a) of f(x), ie, there is a polynomial g(x) with rational coefficients such that f(x)=(x-a)g(x).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Rational roots
  1. Rational root (Replies: 5)

Loading...