Precalculus : Determine the Number of Positive and Negative Real Zeros of a Polynomial Using Descartes' Rule of Signs
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Example Question #1 : Determine The Number Of Positive And Negative Real Zeros Of A Polynomial Using Descartes' Rule Of Signs
Determine the possible number of Positive and Negative Real Zeros of the polynomial using Descartes' Rule of Signs
Positive zeroes:
Negative zeroes:
Positive zeroes:
Negative zeroes:
Positive zeroes:
Negative zeroes:
Positive zeroes:
Negative zeroes:
Positive zeroes:
Negative zeroes:
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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