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Sixth order algebraic equation

  1. May 28, 2007 #1
    I have the following equation (a,b,c real coefficients):

    x^6 + a*x^4 + b*x^2 + c = 0

    How do I do a complete discussion? For example I would like to know if there are six coincident roots, 2 triple roots, distint roots, a pair of complex solution and 4 real coincident solutions and so on.
  2. jcsd
  3. May 28, 2007 #2
    Well for starters that is just a monic cubic in disguise :)
  4. May 28, 2007 #3
    I have noticed it. It can be transformed in the form of a cubic equation (it is sufficient to replace x^2 with y). But I would like if somebody does the complete study in detail.
  5. May 28, 2007 #4


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    well that means do a complete study of cubics and then take square roots of all the roots. i am sure you can do this. or read my algebra book on my website.
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