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A question about zeros of polynomials

  1. Jan 5, 2010 #1
    POlynomials (or Taylor series ) of the form

    [tex] P(x)= \sum_{n}a_{2n}X^{2n} [/tex] with [tex] a_{2n}\ge 0 [/tex] strictly

    have ALWAYS pure imaginary roots ??

    it happens with [tex] sinh(x)/x [/tex] [tex] cos(x) [/tex] could someone provide a counterexample ? is there an hypothesis with this name ??
  2. jcsd
  3. Jan 5, 2010 #2


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    Hi zetafunction! :smile:

    Hint: start by treating it as a polynomial in x2, and factor it as (x2 + z1)(x2 + z2)…(x2 + zn).

    What happens if any of the zs are imaginary? :wink:
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