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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- Jul 21st 2009, 09:57 AMhsachdevahGuessing 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. - Jul 21st 2009, 10:01 AMHallsofIvy
If f(c) and $\displaystyle \lim_{x\rightarrow \infty} f(x)$ 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).