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Descartes Rule of Signs

Rule

Descartes' Rule of Signs

For a polynomial function written in standard form:

  • The number of positive real zeros is equal to the number of sign changes in or less than the first following even number.
  • The number of negative real zeros is equal to the number of sign changes in or less than the first following even number.

For example: According to the rule, the number of positive real zeros can be either since there are two changes in sign, or, because one less than the following even number is still

The function can be factored to and using the zero product property the zeros are given by and Thus, has two real positive zeros as stated by Discartes' rules of signs.