# Proof that rational polynomials have at least one rational root [closed]

Every odd degree polynomial with real coefficient has at least one real root, that i can prove. but i dont know how to prove that every odd degree polynomial with rational coefficients has at least one rational root?

• I'm happy to hear that you can't prove it, because, as M10687. says, this simply isn't true! Jun 8, 2016 at 18:20
• The intermediate value theorem is not true over the rational numbers, see here. So the proof you know will not work. For good reason, because it is no longer true. Jun 8, 2016 at 18:22
• You may be confused about what the en.wikipedia.org/wiki/Rational_root_theorem says, which is "if a polynomial has a rational root, then it satisfies a certain condition" - but it doesn't say all polynomials must have rational roots. Jun 8, 2016 at 23:23
• I'm voting to close this question as off-topic because it asks for the proof of a non-result. Jun 9, 2016 at 1:05

Consider $x^3+ 2$. Does this have a rational root?