Homework Help is Here – Start Your Trial Now!
Math
Algebra
-80 -(2)) lo mes 6 ai12+1 at novie (e 6) Determine the zeros and their multiplicities for f(x) = 2x²(x + 2)(x – 3)² %3D Zeros Multiplicity

-80 -(2)) lo mes 6 ai12+1 at novie (e 6) Determine the zeros and their multiplicities for f(x) = 2x²(x + 2)(x – 3)² %3D Zeros Multiplicity

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
See similar textbooks
icon
Related questions
Question
100%
Title: Determining Zeros and Their Multiplicities To determine the zeros and their multiplicities for the function \( f(x) = 2x^2(x + 2)(x - 3)^2 \), we need to factor the polynomial and analyze each factor. ### Zeros and Multiplicities Below is a table summarizing the zeros and their corresponding multiplicities. | Zeros | Multiplicity | |-------|--------------| | | | | | | | | | - **Zeros**: The values of \( x \) that make the function \( f(x) \) equal to zero. - **Multiplicity**: The number of times a particular zero appears as a root of the polynomial. ### How to Find the Zeros and Multiplicities 1. **Identify the factors of the polynomial**: \( 2x^2(x + 2)(x - 3)^2 \) 2. **Set each factor equal to zero**: - \( 2x^2 = 0 \Rightarrow x = 0 \) - \( x + 2 = 0 \Rightarrow x = -2 \) - \( (x - 3)^2 = 0 \Rightarrow x = 3 \) 3. **Determine the multiplicity of each zero**: - \( x = 0 \) has a multiplicity of \( 2 \) (from \( 2x^2 \)) - \( x = -2 \) has a multiplicity of \( 1 \) (from \( x + 2 \)) - \( x = 3 \) has a multiplicity of \( 2 \) (from \( (x - 3)^2 \)) ### Final Table | Zeros | Multiplicity | |-------|---------------| | 0 | 2 | | -2 | 1 | | 3 | 2 | Now you can accurately determine the zeros and their multiplicities for the given function \( f(x) = 2x^2(x + 2)(x - 3)^2 \).
Transcribed Image Text:Title: Determining Zeros and Their Multiplicities To determine the zeros and their multiplicities for the function \( f(x) = 2x^2(x + 2)(x - 3)^2 \), we need to factor the polynomial and analyze each factor. ### Zeros and Multiplicities Below is a table summarizing the zeros and their corresponding multiplicities. | Zeros | Multiplicity | |-------|--------------| | | | | | | | | | - **Zeros**: The values of \( x \) that make the function \( f(x) \) equal to zero. - **Multiplicity**: The number of times a particular zero appears as a root of the polynomial. ### How to Find the Zeros and Multiplicities 1. **Identify the factors of the polynomial**: \( 2x^2(x + 2)(x - 3)^2 \) 2. **Set each factor equal to zero**: - \( 2x^2 = 0 \Rightarrow x = 0 \) - \( x + 2 = 0 \Rightarrow x = -2 \) - \( (x - 3)^2 = 0 \Rightarrow x = 3 \) 3. **Determine the multiplicity of each zero**: - \( x = 0 \) has a multiplicity of \( 2 \) (from \( 2x^2 \)) - \( x = -2 \) has a multiplicity of \( 1 \) (from \( x + 2 \)) - \( x = 3 \) has a multiplicity of \( 2 \) (from \( (x - 3)^2 \)) ### Final Table | Zeros | Multiplicity | |-------|---------------| | 0 | 2 | | -2 | 1 | | 3 | 2 | Now you can accurately determine the zeros and their multiplicities for the given function \( f(x) = 2x^2(x + 2)(x - 3)^2 \).
Expert Solution
steps

Step by step

Solved in 2 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Polynomial
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, algebra and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:
9780134463216
Author:
Robert F. Blitzer
Publisher:
PEARSON
Contemporary Abstract Algebra
Contemporary Abstract Algebra
Algebra
ISBN:
9781305657960
Author:
Joseph Gallian
Publisher:
Cengage Learning
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
Algebra
ISBN:
9781285463247
Author:
David Poole
Publisher:
Cengage Learning
Algebra And Trigonometry (11th Edition)
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:
9780135163078
Author:
Michael Sullivan
Publisher:
PEARSON
Introduction to Linear Algebra, Fifth Edition
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:
9780980232776
Author:
Gilbert Strang
Publisher:
Wellesley-Cambridge Press
College Algebra (Collegiate Math)
College Algebra (Collegiate Math)
Algebra
ISBN:
9780077836344
Author:
Julie Miller, Donna Gerken
Publisher:
McGraw-Hill Education
SEE MORE TEXTBOOKS