I'm looking for a general non-constructive way (I assume there isn't a constructive way in general) to test if a polynomial with integer coefficients has a zero in [0,1]. I am aware of the rational root theorem, but I don't believe this is useful in all cases.
Could anyone point me toward literature on this subject? Or directly tell me if such a test is possible and/or what it is?
This question can be approached in many ways - sorry if I have tagged incorrectly!