1. Finding Real Roots of Polynomial Equations
6.5
Finding Real Roots of Polynomial Equations

2. -factoring to find real roots -explain Multiplicity
The root 0 has a multiplicity of 3.
The root -3 has a multiplicity of 2.

3. 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.

4. 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.

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

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

7. 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!!!

8. Find all real roots.

9. Find all real roots.

10. Find all real roots.

11. Homework
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