1. Decartes’ Rule of the Signs 33 22 11 Rule Steps Examples

2. Decartes’ Rule of the Signs  The number of sign changes of P(x)=0 is equal to the number of positive real roots of the equation.  The number of sign changes of P(-x)=0 is equal to the number of negative real roots of the equation. 2

3. Steps  Put equation in standard form  Find the number of sign changes  This is the number of positive real roots  Replace “x” with “–x”  Simplify using power rules  Find the number of sign changes  This is the number of negative real roots 3

4. Example What does Decartes’ Rule of the Signs tell you about the real roots of ? 4 + to -

5. Example Cont. What does Decartes’ Rule of the Signs tell you about the real roots of ? 5 No change - to +