Finding Real Roots of Polynomial Equations How do
![Finding Real Roots of Polynomial Equations • How do we identify the multiplicity of Finding Real Roots of Polynomial Equations • How do we identify the multiplicity of](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-1.jpg)
![Finding Real Roots of Polynomial Equations In Lesson 3 -5, you used several methods Finding Real Roots of Polynomial Equations In Lesson 3 -5, you used several methods](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-2.jpg)
![Finding Real Roots of Polynomial Equations Example 1: Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 1: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-3.jpg)
![Finding Real Roots of Polynomial Equations Example 2: Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 2: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-4.jpg)
![Finding Real Roots of Polynomial Equations Example 3: Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 3: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-5.jpg)
![Finding Real Roots of Polynomial Equations Example 4: Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 4: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-6.jpg)
![Finding Real Roots of Polynomial Equations Sometimes a polynomial equation has a factor that Finding Real Roots of Polynomial Equations Sometimes a polynomial equation has a factor that](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-7.jpg)
![Finding Real Roots of Polynomial Equations You cannot always determine the multiplicity of a Finding Real Roots of Polynomial Equations You cannot always determine the multiplicity of a](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-8.jpg)
![Finding Real Roots of Polynomial Equations Example 5: Identifying Multiplicity Identify the roots of Finding Real Roots of Polynomial Equations Example 5: Identifying Multiplicity Identify the roots of](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-9.jpg)
![Finding Real Roots of Polynomial Equations Example 6: Identifying Multiplicity Identify the roots of Finding Real Roots of Polynomial Equations Example 6: Identifying Multiplicity Identify the roots of](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-10.jpg)
![Finding Real Roots of Polynomial Equations Lesson 4. 1 Practice A Holt Mc. Dougal Finding Real Roots of Polynomial Equations Lesson 4. 1 Practice A Holt Mc. Dougal](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-11.jpg)
- Slides: 11
![Finding Real Roots of Polynomial Equations How do we identify the multiplicity of Finding Real Roots of Polynomial Equations • How do we identify the multiplicity of](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-1.jpg)
Finding Real Roots of Polynomial Equations • How do we identify the multiplicity of roots? • How do we use the Rational Root Theorem and the irrational Root Theorem to solve polynomial equations? Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations In Lesson 3 5 you used several methods Finding Real Roots of Polynomial Equations In Lesson 3 -5, you used several methods](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-2.jpg)
Finding Real Roots of Polynomial Equations In Lesson 3 -5, you used several methods for factoring polynomials. As with some quadratic equations, factoring a polynomial equation is one way to find its real roots. Using the Zero Product Property, you can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Example 1 Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 1: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-3.jpg)
Finding Real Roots of Polynomial Equations Example 1: Using Factoring to Solve Polynomial Equations Solve the polynomial equation by factoring. 4 x 6 + 4 x 5 – 24 x 4 = 0 Check using a graph. The roots appear to be located at x = 0, x = – 3, and x = 2. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Example 2 Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 2: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-4.jpg)
Finding Real Roots of Polynomial Equations Example 2: Using Factoring to Solve Polynomial Equations Solve the polynomial equation by factoring. x 4 + 25 = 26 x 2 The roots are 5, – 5, 1, and – 1. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Example 3 Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 3: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-5.jpg)
Finding Real Roots of Polynomial Equations Example 3: Using Factoring to Solve Polynomial Equations Solve the polynomial equation by factoring. 2 x 6 – 10 x 5 – 12 x 4 = 0 The roots are 0, 6, and – 1. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Example 4 Using Factoring to Solve Polynomial Equations Finding Real Roots of Polynomial Equations Example 4: Using Factoring to Solve Polynomial Equations](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-6.jpg)
Finding Real Roots of Polynomial Equations Example 4: Using Factoring to Solve Polynomial Equations Solve the polynomial equation by factoring. x 3 – 2 x 2 – 25 x = – 50 The roots are 5, – 5, and 2. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Sometimes a polynomial equation has a factor that Finding Real Roots of Polynomial Equations Sometimes a polynomial equation has a factor that](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-7.jpg)
Finding Real Roots of Polynomial Equations Sometimes a polynomial equation has a factor that appears more than once. This creates a multiple root. In 3 x 5 + 18 x 4 + 27 x 3 = 0 has two multiple roots, 0 and – 3. For example, the root 0 is a factor three times because 3 x 3 = 0. The multiplicity of root r is the number of times that x – r is a factor of P(x). When a real root has even multiplicity, the graph of y = P(x) touches the x-axis but does not cross it. When a real root has odd multiplicity greater than 1, the graph “bends” as it crosses the x-axis. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations You cannot always determine the multiplicity of a Finding Real Roots of Polynomial Equations You cannot always determine the multiplicity of a](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-8.jpg)
Finding Real Roots of Polynomial Equations You cannot always determine the multiplicity of a root from a graph. It is easiest to determine multiplicity when the polynomial is in factored form. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Example 5 Identifying Multiplicity Identify the roots of Finding Real Roots of Polynomial Equations Example 5: Identifying Multiplicity Identify the roots of](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-9.jpg)
Finding Real Roots of Polynomial Equations Example 5: Identifying Multiplicity Identify the roots of each equation. State the multiplicity of each root. 2 x 4 - 12 x 3 + 18 x 2 = 0 The root 0 has multiplicity of 2, the root 3 has multiplicity of 2. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Example 6 Identifying Multiplicity Identify the roots of Finding Real Roots of Polynomial Equations Example 6: Identifying Multiplicity Identify the roots of](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-10.jpg)
Finding Real Roots of Polynomial Equations Example 6: Identifying Multiplicity Identify the roots of each equation. State the multiplicity of each root. x 3 – x 2 – x + 1 = 0 The root 1 has multiplicity 2, the root -1 has multiplicity 1. Holt Mc. Dougal Algebra 2
![Finding Real Roots of Polynomial Equations Lesson 4 1 Practice A Holt Mc Dougal Finding Real Roots of Polynomial Equations Lesson 4. 1 Practice A Holt Mc. Dougal](https://slidetodoc.com/presentation_image_h/241bde845d17abb0dc79668e1cef681a/image-11.jpg)
Finding Real Roots of Polynomial Equations Lesson 4. 1 Practice A Holt Mc. Dougal Algebra 2
Finding the real roots of polynomial equations
Practice a finding real roots of polynomial equations
Finding real roots of polynomial equations worksheet
Finding real roots of polynomial equations
Finding real roots of polynomial equations
7.2 finding complex solutions of polynomial equations
5-5 theorems about roots of polynomial equations
Use of polynomials in real life
Roots of a polynomial
How to find the indicated real nth roots of a
Chonp
Roots part i