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 $\displaystyle \lim_{x\rightarrow \infty} f(x)$ 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).