Special Case
The subtraction of only multiples of 2 from the maximal number of positive roots occurs because the polynomial may have complex roots, which always come in pairs since the rule applies to polynomials whose coefficients are real. Thus if the polynomial is known to have all real roots, this rule allows one to find the exact number of positive and negative roots. Since it is easy to determine the multiplicity of zero as a root, the sign of all roots can be determined in this case.
Read more about this topic: Descartes' Rule Of Signs
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