1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Find the minimal polynomial with real root

  1. Mar 26, 2009 #1
    Find the minimal polynomial with root 21/3 + 21/2.

    I would just use maple but I do not have it installed on this machine.
    I found the polynomial and verified that this is indeed a root. I only have Eisenstiens criterion for determining whether it is irreducible, and I can not apply it in this case. Do you have another method? I have not tried substituting x=x+1 or x=x-1 or other substitutions.

    The polynomial is x6-6x4-4x3+12x2-24x-4
     
  2. jcsd
  3. Mar 27, 2009 #2

    Hurkyl

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Try computing [itex][ \mathbb{Q}(\sqrt[3]{2} + \sqrt{2}) : \mathbb{Q} ][/itex].

    Or... the dimension of the vector space spanned by powers of [itex]\sqrt[3]{2} + \sqrt{2}[/itex].

    Or... something else that would tell you information about the minimal polynomial.
     
    Last edited: Mar 27, 2009
  4. Mar 27, 2009 #3

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You don't need to show the polynomial is irreducible, do you? You just want to show it has no rational roots. Look at the rational root test. If that has a rational root, the root must divide 4.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Find the minimal polynomial with real root
Loading...