Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form o…
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Chapter 2.3, Problem 76E
To determine

To verify the upper and lower bounds using synthetic division and to determine the real zeros of the function f(x)=2x4−8x+3 .

Upper bound: x=3

Lower bound: x=−4

Expert Solution & Answer
Check Mark

Answer to Problem 76E

  0.38, 1.435

Explanation of Solution

Given:

Function: f(x)=2x4−8x+3

Upper bound: x=3

Lower bound: x=−4

Calculation:

1. Verifying upper bound:

Using synthetic division,

  3200−8361854138261846141

Here, the last row values are positive values or zeros.

Hence, the upper bound of given function is x = 3.

2. Verifying lower bound:

Using synthetic division,

  −4200−83−832−1285442−832−136547

Here, the last row values are alternatively positive and negative.

Hence, the lower bound of given function is x = -4.

3. Calculation of real zeros:

Here, the zeros are calculated using graphical method.

Calculation for graph:

Consider f(x)=2x4−8x+3

    Values of xValues of f (x)
    03
    1-3
    -119
    213
    -251

By taking different values of x, the graph can be plotted.

Graph:

  Precalculus with Limits: A Graphing Approach, Chapter 2.3, Problem 76E

Interpretation:

By observing graph, it is clear that the curve of the function meets x-axis at x=0.38 and 1.435.

Hence, the zeros of the function are x=0.38 and 1.435.

Conclusion:

Therefore, the zeros of given polynomial function are x=0.38 and 1.435.

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Chapter 2.3, Problem 75E
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Chapter 2.3, Problem 77E

Chapter 2 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 10ECh. 2.7 - Prob. 11ECh. 2.7 - Prob. 12ECh. 2.7 - Prob. 13ECh. 2.7 - Prob. 14ECh. 2.7 - Prob. 15ECh. 2.7 - Prob. 16ECh. 2.7 - Prob. 17ECh. 2.7 - Prob. 18ECh. 2.7 - Prob. 19ECh. 2.7 - Prob. 20ECh. 2.7 - Prob. 21ECh. 2.7 - Prob. 22ECh. 2.7 - Prob. 23ECh. 2.7 - Prob. 24ECh. 2.7 - Prob. 25ECh. 2.7 - Prob. 26ECh. 2.7 - Prob. 27ECh. 2.7 - Prob. 28ECh. 2.7 - Prob. 29ECh. 2.7 - Prob. 30ECh. 2.7 - Prob. 31ECh. 2.7 - Prob. 32ECh. 2.7 - Prob. 33ECh. 2.7 - Prob. 34ECh. 2.7 - Prob. 35ECh. 2.7 - Prob. 36ECh. 2.7 - Prob. 37ECh. 2.7 - Prob. 38ECh. 2.7 - Prob. 39ECh. 2.7 - Prob. 40ECh. 2.7 - Prob. 41ECh. 2.7 - Prob. 42ECh. 2.7 - Prob. 43ECh. 2.7 - Prob. 44ECh. 2.7 - Prob. 45ECh. 2.7 - Prob. 46ECh. 2.7 - Prob. 47ECh. 2.7 - Prob. 48ECh. 2.7 - Prob. 49ECh. 2.7 - Prob. 50ECh. 2.7 - Prob. 51ECh. 2.7 - Prob. 52ECh. 2.7 - Prob. 53ECh. 2.7 - Prob. 54ECh. 2.7 - Prob. 55ECh. 2.7 - Prob. 56ECh. 2.7 - Prob. 57ECh. 2.7 - Prob. 58ECh. 2.7 - Prob. 59ECh. 2.7 - Prob. 60ECh. 2.7 - Prob. 61ECh. 2.7 - Prob. 62ECh. 2.7 - Prob. 63ECh. 2.7 - Prob. 64ECh. 2.7 - Prob. 65ECh. 2.7 - Prob. 66ECh. 2.7 - Prob. 67ECh. 2.7 - Prob. 68ECh. 2.7 - Prob. 69ECh. 2.7 - Prob. 70ECh. 2.7 - Prob. 71ECh. 2.7 - Prob. 72ECh. 2.7 - Prob. 73ECh. 2.7 - Prob. 74ECh. 2.7 - Prob. 75ECh. 2.7 - Prob. 76ECh. 2.7 - Prob. 77ECh. 2.7 - Prob. 78ECh. 2.7 - Prob. 79ECh. 2.7 - Prob. 80ECh. 2.7 - Prob. 81ECh. 2.7 - Prob. 82ECh. 2.7 - Prob. 83ECh. 2.7 - Prob. 84ECh. 2.7 - Prob. 85ECh. 2.7 - Prob. 86ECh. 2.7 - Prob. 87ECh. 2.7 - Prob. 88ECh. 2.7 - Prob. 89ECh. 2.7 - Prob. 90ECh. 2.7 - Prob. 91ECh. 2.7 - Prob. 92ECh. 2.7 - Prob. 93ECh. 2.7 - Prob. 94ECh. 2.7 - Prob. 95ECh. 2.7 - Prob. 96ECh. 2.7 - Prob. 97ECh. 2.7 - Prob. 98ECh. 2.7 - Prob. 99ECh. 2.7 - Prob. 100ECh. 2.7 - Prob. 101ECh. 2.7 - Prob. 102ECh. 2.7 - Prob. 103ECh. 2.7 - Prob. 104ECh. 2.7 - Prob. 105ECh. 2.7 - Prob. 106ECh. 2.7 - Prob. 107ECh. 2.8 - Prob. 1ECh. 2.8 - Prob. 2ECh. 2.8 - Prob. 3ECh. 2.8 - Prob. 4ECh. 2.8 - Prob. 5ECh. 2.8 - Prob. 6ECh. 2.8 - Prob. 7ECh. 2.8 - Prob. 8ECh. 2.8 - Prob. 9ECh. 2.8 - Prob. 10ECh. 2.8 - Prob. 11ECh. 2.8 - Prob. 12ECh. 2.8 - Prob. 13ECh. 2.8 - Prob. 14ECh. 2.8 - Prob. 15ECh. 2.8 - Prob. 16ECh. 2.8 - Prob. 17ECh. 2.8 - Prob. 18ECh. 2.8 - Prob. 19ECh. 2.8 - Prob. 20ECh. 2.8 - Prob. 21ECh. 2.8 - Prob. 22ECh. 2.8 - Prob. 23ECh. 2.8 - Prob. 24ECh. 2.8 - Prob. 25ECh. 2.8 - Prob. 26ECh. 2.8 - Prob. 27ECh. 2.8 - Prob. 28ECh. 2.8 - Prob. 29ECh. 2.8 - Prob. 30ECh. 2.8 - Prob. 31ECh. 2.8 - Prob. 32ECh. 2.8 - Prob. 33ECh. 2.8 - Prob. 34ECh. 2.8 - Prob. 35ECh. 2.8 - Prob. 36ECh. 2.8 - Prob. 37ECh. 2.8 - Prob. 38ECh. 2 - Prob. 1RECh. 2 - Prob. 2RECh. 2 - Prob. 3RECh. 2 - Prob. 4RECh. 2 - Prob. 5RECh. 2 - Prob. 6RECh. 2 - Prob. 7RECh. 2 - Prob. 8RECh. 2 - Prob. 9RECh. 2 - Prob. 10RECh. 2 - Prob. 11RECh. 2 - Prob. 12RECh. 2 - Prob. 13RECh. 2 - Prob. 14RECh. 2 - Prob. 15RECh. 2 - Prob. 16RECh. 2 - Prob. 17RECh. 2 - Prob. 18RECh. 2 - Prob. 19RECh. 2 - Prob. 20RECh. 2 - Prob. 21RECh. 2 - Prob. 22RECh. 2 - Prob. 23RECh. 2 - Prob. 24RECh. 2 - Prob. 25RECh. 2 - Prob. 26RECh. 2 - Prob. 27RECh. 2 - Prob. 28RECh. 2 - Prob. 29RECh. 2 - Prob. 30RECh. 2 - Prob. 31RECh. 2 - Prob. 32RECh. 2 - Prob. 33RECh. 2 - Prob. 34RECh. 2 - Prob. 35RECh. 2 - Prob. 36RECh. 2 - Prob. 37RECh. 2 - Prob. 38RECh. 2 - Prob. 39RECh. 2 - Prob. 40RECh. 2 - Prob. 41RECh. 2 - Prob. 42RECh. 2 - Prob. 43RECh. 2 - Prob. 44RECh. 2 - Prob. 45RECh. 2 - Prob. 46RECh. 2 - Prob. 47RECh. 2 - Prob. 48RECh. 2 - Prob. 49RECh. 2 - Prob. 50RECh. 2 - Prob. 51RECh. 2 - Prob. 52RECh. 2 - Prob. 53RECh. 2 - Prob. 54RECh. 2 - Prob. 55RECh. 2 - Prob. 56RECh. 2 - Prob. 57RECh. 2 - Prob. 58RECh. 2 - Prob. 59RECh. 2 - Prob. 60RECh. 2 - Prob. 61RECh. 2 - Prob. 62RECh. 2 - Prob. 63RECh. 2 - Prob. 64RECh. 2 - Prob. 65RECh. 2 - Prob. 66RECh. 2 - Prob. 67RECh. 2 - Prob. 68RECh. 2 - Prob. 69RECh. 2 - Prob. 70RECh. 2 - Prob. 71RECh. 2 - Prob. 72RECh. 2 - Prob. 73RECh. 2 - Prob. 74RECh. 2 - Prob. 75RECh. 2 - Prob. 76RECh. 2 - Prob. 77RECh. 2 - Prob. 78RECh. 2 - Prob. 79RECh. 2 - Prob. 80RECh. 2 - Prob. 81RECh. 2 - Prob. 82RECh. 2 - Prob. 83RECh. 2 - Prob. 84RECh. 2 - Prob. 85RECh. 2 - Prob. 86RECh. 2 - Prob. 87RECh. 2 - Prob. 88RECh. 2 - Prob. 89RECh. 2 - Prob. 90RECh. 2 - Prob. 91RECh. 2 - Prob. 92RECh. 2 - Prob. 93RECh. 2 - Prob. 94RECh. 2 - Prob. 95RECh. 2 - Prob. 96RECh. 2 - Prob. 97RECh. 2 - Prob. 98RECh. 2 - Prob. 99RECh. 2 - Prob. 100RECh. 2 - Prob. 101RECh. 2 - Prob. 102RECh. 2 - Prob. 103RECh. 2 - Prob. 104RECh. 2 - Prob. 105RECh. 2 - Prob. 106RECh. 2 - Prob. 107RECh. 2 - Prob. 108RECh. 2 - Prob. 109RECh. 2 - Prob. 110RECh. 2 - Prob. 111RECh. 2 - Prob. 112RECh. 2 - Prob. 113RECh. 2 - Prob. 114RECh. 2 - Prob. 115RECh. 2 - Prob. 116RECh. 2 - Prob. 117RECh. 2 - Prob. 118RECh. 2 - Prob. 119RECh. 2 - Prob. 120RECh. 2 - Prob. 121RECh. 2 - Prob. 122RECh. 2 - Prob. 123RECh. 2 - Prob. 124RECh. 2 - Prob. 125RECh. 2 - Prob. 126RECh. 2 - Prob. 127RECh. 2 - Prob. 128RECh. 2 - Prob. 129RECh. 2 - Prob. 130RECh. 2 - Prob. 131RECh. 2 - Prob. 132RECh. 2 - Prob. 133RECh. 2 - Prob. 134RECh. 2 - Prob. 135RECh. 2 - Prob. 136RECh. 2 - Prob. 137RECh. 2 - Prob. 138RECh. 2 - Prob. 139RECh. 2 - Prob. 140RECh. 2 - Prob. 141RECh. 2 - Prob. 142RECh. 2 - Prob. 143RECh. 2 - Prob. 144RECh. 2 - Prob. 145RECh. 2 - Prob. 146RECh. 2 - Prob. 147RECh. 2 - Prob. 148RECh. 2 - Prob. 149RECh. 2 - Prob. 150RECh. 2 - Prob. 151RECh. 2 - Prob. 152RECh. 2 - Prob. 153RECh. 2 - Prob. 154RECh. 2 - Prob. 155RECh. 2 - Prob. 156RECh. 2 - Prob. 157RECh. 2 - Prob. 158RECh. 2 - Prob. 159RECh. 2 - Prob. 160RECh. 2 - Prob. 161RECh. 2 - Prob. 162RECh. 2 - Prob. 163RECh. 2 - Prob. 164RECh. 2 - Prob. 165RECh. 2 - Prob. 166RECh. 2 - Prob. 167RECh. 2 - Prob. 168RECh. 2 - Prob. 1CTCh. 2 - Prob. 2CTCh. 2 - Prob. 3CTCh. 2 - Prob. 4CTCh. 2 - Prob. 5CTCh. 2 - Prob. 6CTCh. 2 - Prob. 7CTCh. 2 - Prob. 8CTCh. 2 - Prob. 9CTCh. 2 - Prob. 10CTCh. 2 - Prob. 11CTCh. 2 - Prob. 12CTCh. 2 - Prob. 13CTCh. 2 - Prob. 14CTCh. 2 - Prob. 15CTCh. 2 - Prob. 16CTCh. 2 - Prob. 17CTCh. 2 - Prob. 18CTCh. 2 - Prob. 19CTCh. 2 - Prob. 20CTCh. 2 - Prob. 21CTCh. 2 - Prob. 22CTCh. 2 - Prob. 23CT
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