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Decartes’ Rule of the Signs 33 22 11 Rule Steps Examples
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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
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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
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Example What does Decartes’ Rule of the Signs tell you about the real roots of ? 4 + to -
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Example Cont. What does Decartes’ Rule of the Signs tell you about the real roots of ? 5 No change - to +
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