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**Finding Real Roots of Polynomial Equations**

6.5 Finding Real Roots of Polynomial Equations

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**-factoring to find real roots -explain Multiplicity**

The root 0 has a multiplicity of 3. The root -3 has a multiplicity of 2.

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Multiple Roots Multiple roots appear in a polynomial equation that has a factor that appears more than once. Graph on your calculator. Notice where it touches the x-axis and what it looks like.

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**Rational Root Theorem Every rational root can be written in the form**

Where p is a factor of the constant term q is a factor of the leading coefficient.

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Rational Root Theorem Use the Rational Root Theorem to identify all possible rational roots.

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Rational Root Theorem Use the Rational Root Theorem to identify all possible rational roots.

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**Find all the real roots of each equation.**

Steps: List all possible roots Use synthetic division until you get to a quadratic equation Write the factors ( ) ( ) Write the zeros These steps MUST be shown on all problems!!!

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Find all real roots.

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Find all real roots.

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Find all real roots.

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Homework Page 442 (2-9, 11-14)

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