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Math Help - Guessing Roots of Polynomial

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    Guessing Roots of Polynomial

    Is there any way to tell if a polynomial f(x) has some real root for x>c where c is a real constant.

    I want to predict this without actually calculating the roots.
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  2. #2
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    Quote Originally Posted by hsachdevah View Post
    Is there any way to tell if a polynomial f(x) has some real root for x>c where c is a real constant.

    I want to predict this without actually calculating the roots.
    If f(c) and \lim_{x\rightarrow \infty} f(x) are of different sign, then there must be at least one (in fact an odd number) of roots > c.

    Unfortunately, if they are of the same sign, we do not know whether there are any roots > c (if there are any there must be an even number).
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