Use Descartes' Rule of Signs to determine the number of positive real zeroes, negative real zeroes, and imaginary zeroes.

Descartes' Rule of Signs helps determine the number of positive and negative real roots of a polynomial by counting sign changes in the polynomial and its transformed version. It shows that for a polynomial, the number of positive real roots can vary while negative roots and imaginary roots depend on the total degree of the polynomial. This method allows us to systematically analyze root characteristics effectively.
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Answered by Anonymous | 2025-07-04

Using Descartes' Rule of Signs, we can determine the number of positive and negative real roots as well as imaginary roots from a polynomial. By counting the sign changes of both the original polynomial and the transformed polynomial, it can be established how many roots exist in each category. This method effectively aids in identifying root characteristics based on the polynomial's degree. ;

Answered by GinnyAnswer | 2025-07-04