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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


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    You know that


    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.
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