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!

Homework Help: Finding the minimal polynomial of an irrational over Q

  1. Oct 28, 2016 #1
    1. The problem statement, all variables and given/known data
    Let a = (1+(3)^1/2)^1/2. Find the minimal polynomial of a over Q.

    2. Relevant equations

    3. The attempt at a solution
    Maybe the first thing to realize is that Q(a):Q is probably going to be 4, in order to get rid of both of the square roots in the expression. I also suspect that +/-(3)^1/2 will be roots of the minimal polynomial, as Q(a):Q = [Q(a):Q((3)^1/2)]*[Q(3^1/2):Q]. I do not know where to go from here, any advice PF?
  2. jcsd
  3. Oct 28, 2016 #2


    User Avatar
    Homework Helper

    so your on the right track looking for 4 conjugates
    consider all sign variations of square roots
    the minimum polynomial will be
    where a,b,c,d are the four conjugates
    another possibly easier approach is to isolate 3 in your equation for a
    the minimal polynomial of 3 is
    is the minimal polynomial of a if f(a) is 3 in terms of a
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted