Root finding in [0,1] I am interested in the problem of finding a real root of a polynomial equation $f(x)=0$ where
$f(x)=\sum_{i=0}^n a_ix^i$. Is it possible to give a reduction, i.e, to compute a different polynomial $g$ in polytime such that $f$ has a real root iff $g$ has a real root in [0,1]$?
Here is an alternative to the answer by R B ; It is somewhat simpler, but has the disadvantage of an increase in degree.

Simply take $g(x) = x^{2n}f(x)f(-x)f(1/x)f(-1/x)$.