Descartes Rule of Signs to Determine Number of Positive & Negative Zeros

In this video, Mario from Mario's Math Tutoring explains Descartes' Rule of Signs, a powerful tool for analyzing the possible number of positive and negative real zeros of a polynomial function. Learn how to identify sign changes in the original polynomial to determine the maximum number of positive real zeros. Then, discover how to substitute -x into the function to find the maximum number of negative real zeros. Mario also introduces the concept of imaginary zeros coming in conjugate pairs and how this affects the possible combinations of positive, negative, and imaginary zeros. This video will help you strategically approach finding polynomial zeros and improve your understanding of polynomial behavior.

Timestamps:
00:00 Example 1 f(x)=3x^5-2x^4+x^3-4x-8
0:12 Analyze Sign Changes
0:42 Make a Positive, Negative, Imaginary Chart
1:11 Replace x with (-x) to Analyze the Maximum Number of Negative Zeros
2:05 Discussing Imaginary Conjugate Pairs
3:00 How to Use Descartes Rule of Signs to Narrow Down Finding Zeros

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