Determine the number of positive, negative and complex roots of a polynomial

The video tutorial explains how to determine the possible number of positive, negative, and imaginary zeros of a polynomial using Descartes' Rule of Signs. The instructor demonstrates the process by analyzing sign changes in the polynomial and substituting negative values to find negative zeros. The tutorial concludes with a discussion on the total number of zeros, including complex roots, based on the polynomial's degree.

What is the polynomial function discussed in the text?

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What is the significance of the number of sign changes in determining the number of positive real zeros?

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How many positive real zeros can the polynomial have according to the Descartes' rule of signs?

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What happens to the signs of the terms when substituting negative x into the polynomial?

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What conclusion can be drawn about the number of negative real zeros for the polynomial?

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How many total zeros can the polynomial have based on its degree?

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If one zero is positive, what can be said about the other two zeros?

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