# Descartes' rule of signs

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##### Examples

###### Lessons

**Use Descartes' Rule of Signs to Determine the Number of Positive and Negative Roots**

Use Descartes' Rule of Signs to determine the possible number of positive roots and negative roots:**Use the Rational Roots Theorem, together with Descartes' Rule of Signs, to Find Roots Effectively**

Solve:

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###### Topic Notes

**For a polynomial $P(x)$:**

__Descartes' Rule of Signs__$\bullet$ the number of positive roots = the number of sign changes in $P(x)$, or less than the sign changes by a multiple of 2.

$\bullet$ the number of negative roots = the number of sign changes in $P(-x)$, or less than the sign changes by a multiple of 2.

*Note: Before applying the Descartes' Rule of Signs, make sure to arrange the terms of the polynomial in descending order of exponents.*

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