Algebra and Trigonometry: Structure and Method, Book 2
Algebra and Trigonometry: Structure and Method, Book 2
2000th Edition
ISBN: 9780395977255
Author: MCDOUGAL LITTEL
Publisher: McDougal Littell
bartleby

Videos

Question
Book Icon
Chapter 8.8, Problem 25WE
To determine

To show : the given polynomial has a zero between 1.5 and 1.6 and approximate it to the nearest hundredth.

Expert Solution & Answer
Check Mark

Explanation of Solution

Given information :

The polynomial:

  P(x)=x33x+1

Formula used :

Intermediate-Value Theorem:

If P is a polynomial function with real coefficients, and m is any number between P (a) and P ( b ), then there is at least one number c between a and b for which P ( c ) = m .

Proof :

As per the problem,

Consider the given polynomial:

  P(x)=x33x+1

For x=1.5

     P(x)=x33x+1              [Write the polynomial] P(1.5)= (1.5) 3 3(1.5)+1    [Substitute x=1.5]P(1.5)=0.125

For x=1.6

     P(x)=x33x+1              [Write the polynomial] P(1.5)= (1.5) 3 3(1.5)+1    [Substitute x=1.5]P(1.6)=0.296

As P(1.5)<0 and P(1.6)>0 , there lies at least one number between 1.5 and 1.6 for which P(x)=0

Make a table for 1.5x1.6

  Algebra and Trigonometry: Structure and Method, Book 2, Chapter 8.8, Problem 25WE

The table of values above, shows that the positive root is between 1.53 and 1.54 Since P(1.53) is closer to 0 than P(1.54) , it can be assumed that root is closer to 1.53 . Therefore, to the nearest hundredth, the positive root of P is 1.53 .

So, the polynomial P(x)=x33x+1 has a zero at x=1.53

Chapter 8 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 8.1 - Prob. 11OECh. 8.1 - Prob. 12OECh. 8.1 - Prob. 1WECh. 8.1 - Prob. 2WECh. 8.1 - Prob. 3WECh. 8.1 - Prob. 4WECh. 8.1 - Prob. 5WECh. 8.1 - Prob. 6WECh. 8.1 - Prob. 7WECh. 8.1 - Prob. 8WECh. 8.1 - Prob. 9WECh. 8.1 - Prob. 10WECh. 8.1 - Prob. 11WECh. 8.1 - Prob. 12WECh. 8.1 - Prob. 13WECh. 8.1 - Prob. 14WECh. 8.1 - Prob. 15WECh. 8.1 - Prob. 16WECh. 8.1 - Prob. 17WECh. 8.1 - Prob. 18WECh. 8.1 - Prob. 19WECh. 8.1 - Prob. 20WECh. 8.1 - Prob. 21WECh. 8.1 - Prob. 22WECh. 8.1 - Prob. 23WECh. 8.1 - Prob. 24WECh. 8.1 - Prob. 25WECh. 8.1 - Prob. 1PCh. 8.1 - Prob. 2PCh. 8.1 - Prob. 3PCh. 8.1 - Prob. 4PCh. 8.1 - Prob. 5PCh. 8.1 - Prob. 6PCh. 8.1 - Prob. 7PCh. 8.1 - Prob. 8PCh. 8.1 - Prob. 9PCh. 8.1 - Prob. 10PCh. 8.1 - Prob. 11PCh. 8.1 - Prob. 12PCh. 8.1 - Prob. 13PCh. 8.1 - Prob. 14PCh. 8.1 - Prob. 15PCh. 8.1 - Prob. 16PCh. 8.1 - Prob. 17PCh. 8.1 - Prob. 18PCh. 8.1 - Prob. 19PCh. 8.1 - Prob. 20PCh. 8.1 - Prob. 1MRECh. 8.1 - Prob. 2MRECh. 8.1 - Prob. 3MRECh. 8.1 - Prob. 4MRECh. 8.1 - Prob. 5MRECh. 8.1 - Prob. 6MRECh. 8.1 - Prob. 7MRECh. 8.1 - Prob. 8MRECh. 8.1 - Prob. 9MRECh. 8.2 - Prob. 1OECh. 8.2 - Prob. 2OECh. 8.2 - Prob. 3OECh. 8.2 - Prob. 4OECh. 8.2 - Prob. 5OECh. 8.2 - Prob. 6OECh. 8.2 - Prob. 7OECh. 8.2 - Prob. 8OECh. 8.2 - Prob. 9OECh. 8.2 - Prob. 10OECh. 8.2 - Prob. 11OECh. 8.2 - Prob. 12OECh. 8.2 - Prob. 13OECh. 8.2 - Prob. 14OECh. 8.2 - Prob. 1WECh. 8.2 - Prob. 2WECh. 8.2 - Prob. 3WECh. 8.2 - Prob. 4WECh. 8.2 - Prob. 5WECh. 8.2 - Prob. 6WECh. 8.2 - Prob. 7WECh. 8.2 - Prob. 8WECh. 8.2 - Prob. 9WECh. 8.2 - Prob. 10WECh. 8.2 - Prob. 1PCh. 8.2 - Prob. 2PCh. 8.2 - Prob. 3PCh. 8.2 - Prob. 4PCh. 8.2 - Prob. 5PCh. 8.2 - Prob. 6PCh. 8.2 - Prob. 7PCh. 8.2 - Prob. 8PCh. 8.2 - Prob. 9PCh. 8.2 - Prob. 10PCh. 8.2 - Prob. 11PCh. 8.2 - Prob. 12PCh. 8.2 - Prob. 13PCh. 8.2 - Prob. 14PCh. 8.2 - Prob. 1STCh. 8.2 - Prob. 2STCh. 8.2 - Prob. 3STCh. 8.2 - Prob. 4STCh. 8.2 - Prob. 5STCh. 8.2 - Prob. 6STCh. 8.2 - Prob. 7STCh. 8.3 - Prob. 1OECh. 8.3 - Prob. 2OECh. 8.3 - Prob. 3OECh. 8.3 - Prob. 4OECh. 8.3 - Prob. 5OECh. 8.3 - Prob. 6OECh. 8.3 - Prob. 7OECh. 8.3 - Prob. 8OECh. 8.3 - Prob. 9OECh. 8.3 - Prob. 10OECh. 8.3 - Prob. 11OECh. 8.3 - Prob. 12OECh. 8.3 - Prob. 1WECh. 8.3 - Prob. 2WECh. 8.3 - Prob. 3WECh. 8.3 - Prob. 4WECh. 8.3 - Prob. 5WECh. 8.3 - Prob. 6WECh. 8.3 - Prob. 7WECh. 8.3 - Prob. 8WECh. 8.3 - Prob. 9WECh. 8.3 - Prob. 10WECh. 8.3 - Prob. 11WECh. 8.3 - Prob. 12WECh. 8.3 - Prob. 13WECh. 8.3 - Prob. 14WECh. 8.3 - Prob. 15WECh. 8.3 - Prob. 16WECh. 8.3 - Prob. 17WECh. 8.3 - Prob. 18WECh. 8.3 - Prob. 19WECh. 8.3 - Prob. 20WECh. 8.3 - Prob. 21WECh. 8.3 - Prob. 22WECh. 8.3 - Prob. 23WECh. 8.3 - Prob. 24WECh. 8.3 - Prob. 25WECh. 8.3 - Prob. 26WECh. 8.3 - Prob. 27WECh. 8.3 - Prob. 28WECh. 8.3 - Prob. 29WECh. 8.3 - Prob. 30WECh. 8.3 - Prob. 31WECh. 8.3 - Prob. 32WECh. 8.3 - Prob. 33WECh. 8.3 - Prob. 34WECh. 8.3 - Prob. 1MRECh. 8.3 - Prob. 2MRECh. 8.3 - Prob. 3MRECh. 8.3 - Prob. 4MRECh. 8.3 - Prob. 5MRECh. 8.3 - Prob. 6MRECh. 8.3 - Prob. 7MRECh. 8.3 - Prob. 8MRECh. 8.4 - Prob. 1OECh. 8.4 - Prob. 2OECh. 8.4 - Prob. 3OECh. 8.4 - Prob. 4OECh. 8.4 - Prob. 5OECh. 8.4 - Prob. 6OECh. 8.4 - Prob. 1WECh. 8.4 - Prob. 2WECh. 8.4 - Prob. 3WECh. 8.4 - Prob. 4WECh. 8.4 - Prob. 5WECh. 8.4 - Prob. 6WECh. 8.4 - Prob. 7WECh. 8.4 - Prob. 8WECh. 8.4 - Prob. 9WECh. 8.4 - Prob. 10WECh. 8.4 - Prob. 11WECh. 8.4 - Prob. 12WECh. 8.4 - Prob. 13WECh. 8.4 - Prob. 14WECh. 8.4 - Prob. 15WECh. 8.4 - Prob. 16WECh. 8.4 - Prob. 17WECh. 8.4 - Prob. 18WECh. 8.4 - Prob. 19WECh. 8.4 - Prob. 20WECh. 8.4 - Prob. 21WECh. 8.4 - Prob. 22WECh. 8.4 - Prob. 23WECh. 8.4 - Prob. 24WECh. 8.4 - Prob. 1ECh. 8.4 - Prob. 2ECh. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.5 - Prob. 1OECh. 8.5 - Prob. 2OECh. 8.5 - Prob. 3OECh. 8.5 - Prob. 4OECh. 8.5 - Prob. 5OECh. 8.5 - Prob. 6OECh. 8.5 - Prob. 1WECh. 8.5 - Prob. 2WECh. 8.5 - Prob. 3WECh. 8.5 - Prob. 4WECh. 8.5 - Prob. 5WECh. 8.5 - Prob. 6WECh. 8.5 - Prob. 7WECh. 8.5 - Prob. 8WECh. 8.5 - Prob. 9WECh. 8.5 - Prob. 10WECh. 8.5 - Prob. 11WECh. 8.5 - Prob. 12WECh. 8.5 - Prob. 13WECh. 8.5 - Prob. 14WECh. 8.5 - Prob. 15WECh. 8.5 - Prob. 16WECh. 8.5 - Prob. 17WECh. 8.5 - Prob. 18WECh. 8.5 - Prob. 19WECh. 8.5 - Prob. 20WECh. 8.5 - Prob. 21WECh. 8.5 - Prob. 22WECh. 8.5 - Prob. 23WECh. 8.5 - Prob. 24WECh. 8.5 - Prob. 25WECh. 8.5 - Prob. 26WECh. 8.5 - Prob. 27WECh. 8.5 - Prob. 28WECh. 8.5 - Prob. 29WECh. 8.5 - Prob. 30WECh. 8.5 - Prob. 31WECh. 8.5 - Prob. 32WECh. 8.5 - Prob. 33WECh. 8.5 - Prob. 34WECh. 8.5 - Prob. 35WECh. 8.5 - Prob. 36WECh. 8.5 - Prob. 37WECh. 8.5 - Prob. 38WECh. 8.5 - Prob. 39WECh. 8.5 - Prob. 1MRECh. 8.5 - Prob. 2MRECh. 8.5 - Prob. 3MRECh. 8.5 - Prob. 4MRECh. 8.5 - Prob. 5MRECh. 8.5 - Prob. 6MRECh. 8.5 - Prob. 7MRECh. 8.5 - Prob. 8MRECh. 8.5 - Prob. 9MRECh. 8.6 - Prob. 1OECh. 8.6 - Prob. 2OECh. 8.6 - Prob. 3OECh. 8.6 - Prob. 4OECh. 8.6 - Prob. 5OECh. 8.6 - Prob. 6OECh. 8.6 - Prob. 7OECh. 8.6 - Prob. 8OECh. 8.6 - Prob. 9OECh. 8.6 - Prob. 10OECh. 8.6 - Prob. 11OECh. 8.6 - Prob. 12OECh. 8.6 - Prob. 13OECh. 8.6 - Prob. 14OECh. 8.6 - Prob. 15OECh. 8.6 - Prob. 1WECh. 8.6 - Prob. 2WECh. 8.6 - Prob. 3WECh. 8.6 - Prob. 4WECh. 8.6 - Prob. 5WECh. 8.6 - Prob. 6WECh. 8.6 - Prob. 7WECh. 8.6 - Prob. 8WECh. 8.6 - Prob. 9WECh. 8.6 - Prob. 10WECh. 8.6 - Prob. 11WECh. 8.6 - Prob. 12WECh. 8.6 - Prob. 13WECh. 8.6 - Prob. 14WECh. 8.6 - Prob. 15WECh. 8.6 - Prob. 16WECh. 8.6 - Prob. 17WECh. 8.6 - Prob. 18WECh. 8.6 - Prob. 19WECh. 8.6 - Prob. 20WECh. 8.6 - Prob. 21WECh. 8.6 - Prob. 22WECh. 8.6 - Prob. 23WECh. 8.6 - Prob. 24WECh. 8.6 - Prob. 25WECh. 8.6 - Prob. 26WECh. 8.6 - Prob. 27WECh. 8.6 - Prob. 28WECh. 8.6 - Prob. 29WECh. 8.6 - Prob. 1STCh. 8.6 - Prob. 2STCh. 8.6 - Prob. 3STCh. 8.6 - Prob. 4STCh. 8.6 - Prob. 5STCh. 8.6 - Prob. 6STCh. 8.6 - Prob. 7STCh. 8.7 - Prob. 1OECh. 8.7 - Prob. 2OECh. 8.7 - Prob. 3OECh. 8.7 - Prob. 4OECh. 8.7 - Prob. 5OECh. 8.7 - Prob. 6OECh. 8.7 - Prob. 7OECh. 8.7 - Prob. 8OECh. 8.7 - Prob. 9OECh. 8.7 - Prob. 10OECh. 8.7 - Prob. 11OECh. 8.7 - Prob. 12OECh. 8.7 - Prob. 13OECh. 8.7 - Prob. 14OECh. 8.7 - Prob. 15OECh. 8.7 - Prob. 16OECh. 8.7 - Prob. 1WECh. 8.7 - Prob. 2WECh. 8.7 - Prob. 3WECh. 8.7 - Prob. 4WECh. 8.7 - Prob. 5WECh. 8.7 - Prob. 6WECh. 8.7 - Prob. 7WECh. 8.7 - Prob. 8WECh. 8.7 - Prob. 9WECh. 8.7 - Prob. 10WECh. 8.7 - Prob. 11WECh. 8.7 - Prob. 12WECh. 8.7 - Prob. 13WECh. 8.7 - Prob. 14WECh. 8.7 - Prob. 15WECh. 8.7 - Prob. 16WECh. 8.7 - Prob. 17WECh. 8.7 - Prob. 18WECh. 8.7 - Prob. 19WECh. 8.7 - Prob. 20WECh. 8.7 - Prob. 21WECh. 8.7 - Prob. 22WECh. 8.7 - Prob. 23WECh. 8.7 - Prob. 24WECh. 8.7 - Prob. 25WECh. 8.7 - Prob. 26WECh. 8.7 - Prob. 27WECh. 8.7 - Prob. 28WECh. 8.7 - Prob. 1MRECh. 8.7 - Prob. 2MRECh. 8.7 - Prob. 3MRECh. 8.7 - Prob. 4MRECh. 8.7 - Prob. 5MRECh. 8.7 - Prob. 6MRECh. 8.7 - Prob. 7MRECh. 8.7 - Prob. 8MRECh. 8.7 - Prob. 9MRECh. 8.7 - Prob. 10MRECh. 8.8 - Prob. 1OECh. 8.8 - Prob. 2OECh. 8.8 - Prob. 3OECh. 8.8 - Prob. 4OECh. 8.8 - Prob. 5OECh. 8.8 - Prob. 6OECh. 8.8 - Prob. 7OECh. 8.8 - Prob. 8OECh. 8.8 - Prob. 1WECh. 8.8 - Prob. 2WECh. 8.8 - Prob. 3WECh. 8.8 - Prob. 4WECh. 8.8 - Prob. 5WECh. 8.8 - Prob. 6WECh. 8.8 - Prob. 7WECh. 8.8 - Prob. 8WECh. 8.8 - Prob. 9WECh. 8.8 - Prob. 10WECh. 8.8 - Prob. 11WECh. 8.8 - Prob. 12WECh. 8.8 - Prob. 13WECh. 8.8 - Prob. 14WECh. 8.8 - Prob. 15WECh. 8.8 - Prob. 16WECh. 8.8 - Prob. 17WECh. 8.8 - Prob. 18WECh. 8.8 - Prob. 19WECh. 8.8 - Prob. 20WECh. 8.8 - Prob. 21WECh. 8.8 - Prob. 22WECh. 8.8 - Prob. 23WECh. 8.8 - Prob. 24WECh. 8.8 - Prob. 25WECh. 8.8 - Prob. 26WECh. 8.8 - Prob. 27WECh. 8.8 - Prob. 28WECh. 8.8 - Prob. 29WECh. 8.8 - Prob. 30WECh. 8.8 - Prob. 1ECh. 8.8 - Prob. 2ECh. 8.8 - Prob. 3ECh. 8.8 - Prob. 4ECh. 8.9 - Prob. 1OECh. 8.9 - Prob. 2OECh. 8.9 - Prob. 3OECh. 8.9 - Prob. 1WECh. 8.9 - Prob. 2WECh. 8.9 - Prob. 3WECh. 8.9 - Prob. 4WECh. 8.9 - Prob. 5WECh. 8.9 - Prob. 6WECh. 8.9 - Prob. 7WECh. 8.9 - Prob. 8WECh. 8.9 - Prob. 9WECh. 8.9 - Prob. 10WECh. 8.9 - Prob. 11WECh. 8.9 - Prob. 12WECh. 8.9 - Prob. 13WECh. 8.9 - Prob. 14WECh. 8.9 - Prob. 15WECh. 8.9 - Prob. 16WECh. 8.9 - Prob. 17WECh. 8.9 - Prob. 18WECh. 8.9 - Prob. 19WECh. 8.9 - Prob. 20WECh. 8.9 - Prob. 21WECh. 8.9 - Prob. 22WECh. 8.9 - Prob. 23WECh. 8.9 - Prob. 24WECh. 8.9 - Prob. 25WECh. 8.9 - Prob. 26WECh. 8.9 - Prob. 27WECh. 8.9 - Prob. 28WECh. 8.9 - Prob. 29WECh. 8.9 - Prob. 30WECh. 8.9 - Prob. 1CECh. 8.9 - Prob. 2CECh. 8.9 - Prob. 3CECh. 8.9 - Prob. 4CECh. 8.9 - Prob. 5CECh. 8.9 - Prob. 1STCh. 8.9 - Prob. 2STCh. 8.9 - Prob. 3STCh. 8.9 - Prob. 4STCh. 8.9 - Prob. 5STCh. 8 - Prob. 1CRCh. 8 - Prob. 2CRCh. 8 - Prob. 3CRCh. 8 - Prob. 4CRCh. 8 - Prob. 5CRCh. 8 - Prob. 6CRCh. 8 - Prob. 7CRCh. 8 - Prob. 8CRCh. 8 - Prob. 9CRCh. 8 - Prob. 10CRCh. 8 - Prob. 11CRCh. 8 - Prob. 12CRCh. 8 - Prob. 13CRCh. 8 - Prob. 1CTCh. 8 - Prob. 2CTCh. 8 - Prob. 3CTCh. 8 - Prob. 4CTCh. 8 - Prob. 5CTCh. 8 - Prob. 6CTCh. 8 - Prob. 7CTCh. 8 - Prob. 8CTCh. 8 - Prob. 9CT
Knowledge Booster
Background pattern image
Algebra
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
Text book image
Algebra and Trigonometry (6th Edition)
Algebra
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:PEARSON
Text book image
Contemporary Abstract Algebra
Algebra
ISBN:9781305657960
Author:Joseph Gallian
Publisher:Cengage Learning
Text book image
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Text book image
Algebra And Trigonometry (11th Edition)
Algebra
ISBN:9780135163078
Author:Michael Sullivan
Publisher:PEARSON
Text book image
Introduction to Linear Algebra, Fifth Edition
Algebra
ISBN:9780980232776
Author:Gilbert Strang
Publisher:Wellesley-Cambridge Press
Text book image
College Algebra (Collegiate Math)
Algebra
ISBN:9780077836344
Author:Julie Miller, Donna Gerken
Publisher:McGraw-Hill Education
Evaluating Indefinite Integrals; Author: Professor Dave Explains;https://www.youtube.com/watch?v=-xHA2RjVkwY;License: Standard YouTube License, CC-BY
Calculus - Lesson 16 | Indefinite and Definite Integrals | Don't Memorise; Author: Don't Memorise;https://www.youtube.com/watch?v=bMnMzNKL9Ks;License: Standard YouTube License, CC-BY