Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
1st Edition
ISBN: 9780078682278
Author: McGraw-Hill, Berchie Holliday
Publisher: Glencoe/McGraw-Hill
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Chapter 4.1, Problem 34E
To determine

To write:a polynomial equation of least degree for 2,0.5,4 and find the degree as even or odd. Also find the times graph of the related function cross the x-axis.

Expert Solution & Answer
Check Mark

Answer to Problem 34E

  2x33x218x8=0

The degree of this equation is 3, odd degree

Since all the 3 roots are real, the graph will cross the x-axis thrice

Explanation of Solution

Given information: 2,0.5,4

Calculation:

If x=2, then

  x+2 is  a factor of the polynomial.

If x=0.5, then x=12

  2x=1,

Then, 2x+1 is a factor of the polynomial.

Likewise, if x=4 then x4 is a factor of the polynomial.

Therefore, the linear factors for the polynomial are

  (x+2)(2x+1)(x4)

Now find the product of these factors.

  (x+2)(2x+1)(x4)=0

Multiply the factors

  (x+2)(x4)(2x+1)=0(x22x8)(2x+1)=02x34x216x+x22x8=02x33x218x8=0

A polynomial equation with roots 2,0.5,4 is

  2x33x218x8=0

The degree of this equation is 3. Thus the equation has an odddegree since 3 is an odd number.

Since all the 3 roots are real, the graph will cross the x-axis thrice.

Chapter 4 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 4.1 - Prob. 11CFUCh. 4.1 - Prob. 12CFUCh. 4.1 - Prob. 13CFUCh. 4.1 - Prob. 14CFUCh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.2 - Prob. 1CFUCh. 4.2 - Prob. 2CFUCh. 4.2 - Prob. 3CFUCh. 4.2 - Prob. 4CFUCh. 4.2 - Prob. 5CFUCh. 4.2 - Prob. 6CFUCh. 4.2 - Prob. 7CFUCh. 4.2 - Prob. 8CFUCh. 4.2 - Prob. 9CFUCh. 4.2 - Prob. 10CFUCh. 4.2 - Prob. 11CFUCh. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Prob. 21ECh. 4.2 - Prob. 22ECh. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Prob. 28ECh. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - Prob. 41ECh. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.3 - Prob. 1CFUCh. 4.3 - Prob. 2CFUCh. 4.3 - Prob. 3CFUCh. 4.3 - Prob. 4CFUCh. 4.3 - Prob. 5CFUCh. 4.3 - Prob. 6CFUCh. 4.3 - Prob. 7CFUCh. 4.3 - Prob. 8CFUCh. 4.3 - Prob. 9CFUCh. 4.3 - Prob. 10CFUCh. 4.3 - Prob. 11CFUCh. 4.3 - Prob. 12CFUCh. 4.3 - Prob. 13CFUCh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - Prob. 16ECh. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - Prob. 19ECh. 4.3 - Prob. 20ECh. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - Prob. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 4.3 - Prob. 26ECh. 4.3 - Prob. 27ECh. 4.3 - Prob. 28ECh. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Prob. 31ECh. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Prob. 35ECh. 4.3 - Prob. 36ECh. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Prob. 40ECh. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - Prob. 44ECh. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - Prob. 49ECh. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 1GCECh. 4.3 - Prob. 2GCECh. 4.3 - Prob. 3GCECh. 4.3 - Prob. 4GCECh. 4.3 - Prob. 5GCECh. 4.4 - Prob. 1CFUCh. 4.4 - Prob. 2CFUCh. 4.4 - Prob. 3CFUCh. 4.4 - Prob. 4CFUCh. 4.4 - Prob. 5CFUCh. 4.4 - Prob. 6CFUCh. 4.4 - Prob. 7CFUCh. 4.4 - Prob. 8CFUCh. 4.4 - Prob. 9CFUCh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - Prob. 12ECh. 4.4 - Prob. 13ECh. 4.4 - Prob. 14ECh. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - Prob. 25ECh. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - Prob. 28ECh. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 1MCQCh. 4.4 - Prob. 2MCQCh. 4.4 - Prob. 3MCQCh. 4.4 - Prob. 4MCQCh. 4.4 - Prob. 5MCQCh. 4.4 - Prob. 6MCQCh. 4.4 - Prob. 7MCQCh. 4.4 - Prob. 8MCQCh. 4.4 - Prob. 9MCQCh. 4.4 - Prob. 10MCQCh. 4.5 - Prob. 1CFUCh. 4.5 - Prob. 2CFUCh. 4.5 - Prob. 3CFUCh. 4.5 - Prob. 4CFUCh. 4.5 - Prob. 5CFUCh. 4.5 - Prob. 6CFUCh. 4.5 - Prob. 7CFUCh. 4.5 - Prob. 8CFUCh. 4.5 - Prob. 9CFUCh. 4.5 - Prob. 10CFUCh. 4.5 - Prob. 11CFUCh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Prob. 19ECh. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Prob. 23ECh. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Prob. 27ECh. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Prob. 30ECh. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Prob. 40ECh. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.6 - Prob. 1CFUCh. 4.6 - Prob. 2CFUCh. 4.6 - Prob. 3CFUCh. 4.6 - Prob. 4CFUCh. 4.6 - Prob. 5CFUCh. 4.6 - Prob. 6CFUCh. 4.6 - Prob. 7CFUCh. 4.6 - Prob. 8CFUCh. 4.6 - Prob. 9CFUCh. 4.6 - Prob. 10CFUCh. 4.6 - Prob. 11CFUCh. 4.6 - Prob. 12ECh. 4.6 - Prob. 13ECh. 4.6 - Prob. 14ECh. 4.6 - Prob. 15ECh. 4.6 - Prob. 16ECh. 4.6 - Prob. 17ECh. 4.6 - Prob. 18ECh. 4.6 - Prob. 19ECh. 4.6 - Prob. 20ECh. 4.6 - Prob. 21ECh. 4.6 - Prob. 22ECh. 4.6 - Prob. 23ECh. 4.6 - Prob. 24ECh. 4.6 - Prob. 25ECh. 4.6 - Prob. 26ECh. 4.6 - Prob. 27ECh. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - Prob. 30ECh. 4.6 - Prob. 31ECh. 4.6 - Prob. 32ECh. 4.6 - Prob. 33ECh. 4.6 - Prob. 34ECh. 4.6 - Prob. 35ECh. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Prob. 40ECh. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Prob. 44ECh. 4.6 - Prob. 45ECh. 4.6 - Prob. 46ECh. 4.6 - Prob. 47ECh. 4.6 - Prob. 48ECh. 4.6 - Prob. 49ECh. 4.6 - Prob. 50ECh. 4.6 - Prob. 51ECh. 4.6 - Prob. 52ECh. 4.6 - Prob. 53ECh. 4.6 - Prob. 54ECh. 4.6 - Prob. 55ECh. 4.6 - Prob. 56ECh. 4.6 - Prob. 57ECh. 4.7 - Prob. 1CFUCh. 4.7 - Prob. 2CFUCh. 4.7 - Prob. 3CFUCh. 4.7 - Prob. 4CFUCh. 4.7 - Prob. 5CFUCh. 4.7 - Prob. 6CFUCh. 4.7 - Prob. 7CFUCh. 4.7 - Prob. 8CFUCh. 4.7 - Prob. 9CFUCh. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Prob. 27ECh. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.7 - Prob. 35ECh. 4.7 - Prob. 36ECh. 4.7 - Prob. 37ECh. 4.7 - Prob. 38ECh. 4.7 - Prob. 39ECh. 4.7 - Prob. 40ECh. 4.7 - Prob. 41ECh. 4.7 - Prob. 42ECh. 4.7 - Prob. 43ECh. 4.7 - Prob. 44ECh. 4.7 - Prob. 45ECh. 4.7 - Prob. 46ECh. 4.7 - Prob. 47ECh. 4.7 - Prob. 48ECh. 4.7 - Prob. 49ECh. 4.7 - Prob. 50ECh. 4.7 - Prob. 51ECh. 4.8 - Prob. 1CFUCh. 4.8 - Prob. 2CFUCh. 4.8 - Prob. 3CFUCh. 4.8 - Prob. 4CFUCh. 4.8 - Prob. 5CFUCh. 4.8 - Prob. 6CFUCh. 4.8 - Prob. 7CFUCh. 4.8 - Prob. 8ECh. 4.8 - Prob. 9ECh. 4.8 - Prob. 10ECh. 4.8 - Prob. 11ECh. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.8 - Prob. 18ECh. 4.8 - Prob. 19ECh. 4.8 - Prob. 20ECh. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - Prob. 23ECh. 4.8 - Prob. 24ECh. 4.8 - Prob. 25ECh. 4.8 - Prob. 26ECh. 4.8 - Prob. 27ECh. 4.8 - Prob. 28ECh. 4.8 - Prob. 29ECh. 4.8B - Prob. 1GCECh. 4.8B - Prob. 2GCECh. 4.8B - Prob. 3GCECh. 4.8B - Prob. 4GCECh. 4.8B - Prob. 5GCECh. 4 - Prob. 1SGACh. 4 - Prob. 2SGACh. 4 - Prob. 3SGACh. 4 - Prob. 4SGACh. 4 - Prob. 5SGACh. 4 - Prob. 6SGACh. 4 - Prob. 7SGACh. 4 - Prob. 8SGACh. 4 - Prob. 9SGACh. 4 - Prob. 10SGACh. 4 - Prob. 11SGACh. 4 - Prob. 12SGACh. 4 - Prob. 13SGACh. 4 - Prob. 14SGACh. 4 - Prob. 15SGACh. 4 - Prob. 16SGACh. 4 - Prob. 17SGACh. 4 - Prob. 18SGACh. 4 - Prob. 19SGACh. 4 - Prob. 20SGACh. 4 - Prob. 21SGACh. 4 - Prob. 22SGACh. 4 - Prob. 23SGACh. 4 - Prob. 24SGACh. 4 - Prob. 25SGACh. 4 - Prob. 26SGACh. 4 - Prob. 27SGACh. 4 - Prob. 28SGACh. 4 - Prob. 29SGACh. 4 - Prob. 30SGACh. 4 - Prob. 31SGACh. 4 - Prob. 32SGACh. 4 - Prob. 33SGACh. 4 - Prob. 34SGACh. 4 - Prob. 35SGACh. 4 - Prob. 36SGACh. 4 - Prob. 37SGACh. 4 - Prob. 38SGACh. 4 - Prob. 39SGACh. 4 - Prob. 40SGACh. 4 - Prob. 41SGACh. 4 - Prob. 42SGACh. 4 - Prob. 43SGACh. 4 - Prob. 44SGACh. 4 - Prob. 45SGACh. 4 - Prob. 46SGACh. 4 - Prob. 47SGACh. 4 - Prob. 48SGACh. 4 - Prob. 49SGACh. 4 - Prob. 50SGACh. 4 - Prob. 51SGACh. 4 - Prob. 52SGACh. 4 - Prob. 53SGACh. 4 - Prob. 54SGACh. 4 - Prob. 55SGACh. 4 - Prob. 56SGACh. 4 - Prob. 57SGACh. 4 - Prob. 58SGACh. 4 - Prob. 59SGACh. 4 - Prob. 1SAPCh. 4 - Prob. 2SAPCh. 4 - Prob. 3SAPCh. 4 - Prob. 4SAPCh. 4 - Prob. 5SAPCh. 4 - Prob. 6SAPCh. 4 - Prob. 7SAPCh. 4 - Prob. 8SAPCh. 4 - Prob. 9SAPCh. 4 - Prob. 10SAP
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