Determine the Number of Positive and Negative Real Zeros of a Polynomial Using Descartes' Rule of Signs - Pre-Calculus
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Determine the possible number of Positive and Negative Real Zeros of the polynomial using Descartes' Rule of Signs
Determine the possible number of Positive and Negative Real Zeros of the polynomial using Descartes' Rule of Signs
In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial. The number of real zeroes can then be any positive difference of that number and a positive multiple of two.
For the function
there are four sign changes. As such, the number of positive real zeroes can be
In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial after substituting for 
The number of real zeroes can then be any positive difference of that number and a positive multiple of two.
After substituting 
we get
and there is one sign change.
As such, there can only be one negative root.
In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial. The number of real zeroes can then be any positive difference of that number and a positive multiple of two.
For the function
there are four sign changes. As such, the number of positive real zeroes can be
In order to determine the positive number of real zeroes, we must count the number of sign changes in the coefficients of the terms of the polynomial after substituting for
After substituting
and there is one sign change.
As such, there can only be one negative root.
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