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Poly function of degree n with no roots

  1. Dec 23, 2009 #1
    1. The problem statement, all variables and given/known data

    (a) If n is even find a polynomial function of degree n with n roots.
    (b) If n is odd find one with only one root.

    2. Relevant equations

    3. The attempt at a solution

    If by no roots, they mean no real roots then I guess:
    [tex] f(x) = x^n+1[/tex] would work for both even and odd n's.
    The roots would be i and -i if n is even, and -1, and two complex roots if it's odd..

    Suggestions are very welcome :)
  2. jcsd
  3. Dec 23, 2009 #2


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    Science Advisor

    Yes, that looks to me to be a perfectly good answer. However, "The roots would be i and -i if n is even, and -1, and two complex roots if it's odd" is true only for n= 2 and 3. For general n, if n is even, then all n roots are non-real, i and -i being two of the. If n is odd, -1 is a root and the other n-1 roots are non-real.
  4. Dec 23, 2009 #3
    Ah, I should have stated that, thank you.
    You are usually the one that answers all questions I post around here. It's incredible that you do that for free..You should set up a paypal account :)
    Thanks again.
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