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Math Help - Are there any characteristics of polynomials with rational roots?

  1. #1
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    Are there any characteristics of polynomials with rational roots?

    In a few days im having a presentation in number theory.

    Are there any characteristics of polynomials with rational roots? Both the expression and graphical.

    How do I do this?
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  2. #2
    Senior Member jakncoke's Avatar
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    Re: Are there any characteristics of polynomials with rational roots?

    Like what do you mean.

    Like this one? Assume deg(f(x)) \geq 2

    if  f(x) \in \mathbb{Q}[X] \text{ such that f(x) is irreducible in } \mathbb{Q}[X] \text{ then f has no roots in } \mathbb{Q} ?

    or

     f(x) \in \mathbb{Z}[X] \text{ if f(x) is reducible in } \mathbb{Q}[X] \text{ then f(x) is reducible in also} \mathbb{Z}[X]
    Last edited by jakncoke; December 15th 2012 at 04:55 AM.
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    Re: Are there any characteristics of polynomials with rational roots?

    Sorry, didnt get that :P

    But the teacher gave me a tip
    x^2+px+q=0
    x=r1 V x=r2


    (x-r1)(x-r2)=x2-x(r1+r2)+r2*r1
    p=-(r2+r1)
    q=r2*r1
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  4. #4
    Senior Member jakncoke's Avatar
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    Re: Are there any characteristics of polynomials with rational roots?

    Check out the rational root theorem
    Rational root theorem - Wikipedia, the free encyclopedia
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