在這篇論文中，我們關心的是關於多項式的振動域跟穩定域。在第二節中，我們找到了四次多項式的穩定域，也就是四次多項式的根的絕對值小於1的區域。在第三節中，我們找到了五次多項式的穩定域，也就是五次多項式沒有正根的區域。而在第三節中，我們使用了envelopes的方法。

ABSTRACT
In this thesis, we are concerned with the stability
and oscillation regions of polynomials. In Section 2,
given an arbitrary real quartic polynomial, we find the
exact region containing the coefficients of the polynomial
such that all roots have absolute value less than
1. In Section 3, given an arbitrary real quintic polynomial,
we are concerned with the necessary and suf-
ficient conditions imposed on the parameters of the
polynomial so that all its roots are non-positive. By
means of the method of envelopes, we are able to derive
the exact region containing these parameters.

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