Hello I am working on high order polynomials and I have two questions: 1. Is there a method other than the one based on the "synthetic division with testing the signs" for identifying the lower and upper limits of the real roots? 2. Is there a way for identifying the smallest interval on the x-axis between two successive real roots, i.e. is there a theorem or test that can provide a limit on the size of the x-interval that separates successive real roots without knowing the roots? Thank you for your help!