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Classifcation of irreducible polynomials

  1. Sep 26, 2005 #1
    "Conjecture a classifucation rule for all irreducible polynomials of the form ax^2 + bx + c over the reals. Prove it."

    I'm stuck cold at the start. classification rule ?

    "Let R be an integral domain.
    A nonzero f in R[x] is irreducible provided f is not a unit and in every factorization f = gh, either g or h is a unit in R[x].

    So, f in R[x] is reducible over R if it can be factorised as f = gh where g,h are in R[x] with deg(g) < deg(f) and deg(h) < deg(f). And irreducible otherwise."

    I have no idea where to start, I tried playing with extensions but that seems pointless in the reals.

    For some p, b^2 - 4ac < 0 then p is irreducible over R. But that's not getting me anywhere.

    Could someone please just give me a tiny hint/word which may shed a ray of light? o:)

    Thanks :blushing:
     
  2. jcsd
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