1. Limited time only! Sign up for a free 30min personal 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!

Given min. polynomial of a, find min. polynomial of 1/a

  1. Dec 8, 2012 #1
    1. The problem statement, all variables and given/known data
    Given that the minimal polynomial of a over rationals is x^4+x+8, find the minimal polynomial for 1/a over Q.


    2. Relevant equations
    I know there is a lot of work done out there for finding the min. polynomials of a^k for k>0, however I've never seen anything with a^k for k<0. I have no intuition where to start with this problem, just wondering if there are methods out there.
     
  2. jcsd
  3. Dec 8, 2012 #2
    You know that

    [tex]a^4+a+8=0[/tex]

    An obvious thing to do is to multiply both sides by [itex]\frac{1}{a}[/itex] multiple times.
     
  4. Dec 8, 2012 #3
    Yea I realized this soon after posting, thanks for the help anyway.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Given min. polynomial of a, find min. polynomial of 1/a
Loading...