Abstract
ABSTRACTIn this thesis, we are concerned with the stabilityand oscillation regions of polynomials. In Section 2,given an arbitrary real quartic polynomial, we find theexact region containing the coefficients of the polynomialsuch that all roots have absolute value less than1. In Section 3, given an arbitrary real quintic polynomial,we are concerned with the necessary and suf-ficient conditions imposed on the parameters of thepolynomial so that all its roots are non-positive. Bymeans of the method of envelopes, we are able to derivethe exact region containing these parameters.