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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Chapter 2.5, Problem 67E

a.

To determine

Find the real zeros of the function h(x)=8x3−14x2+18x−9 using graphical method.

a.

Expert Solution
Check Mark

Answer to Problem 67E

  34

Explanation of Solution

Given:

Function: h(x)=8x3−14x2+18x−9

Calculation for graph:

Consider h(x)=8x3−14x2+18x−9

    Values of xValues of h(x)
    0-9
    13
    -1-49
    235
    -2-165

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

Graph:

  Precalculus with Limits: A Graphing Approach, Chapter 2.5, Problem 67E

Interpretation:

By observing graph, it is clear that the curve of the function meets x-axis at x=34.

Hence, the real zeros of the function are x=34.

Conclusion:

Therefore, the real zeros of given polynomial function are x=34.

b.

To determine

By using real zeros of the function h(x)=8x3−14x2+18x−9 , find the imaginary roots.

b.

Expert Solution
Check Mark

Answer to Problem 67E

  34,1+5i2,1−5i2

Explanation of Solution

Given:

Function: h(x)=8x3−14x2+18x−9

Calculation:

From above answer, the real zeros of function are x=34.

Now divide given function with above zero.

Using synthetic division,

  348−1418−96−698−8120 ←Remainder

So, quotient is 8x2−8x+12 and remainder is 0.

So, h(x) factors as

  ⇒h(x)=(x−3)(8x2−8x+12)

To find other zeros, put 8x2−8x+12=0,

The above polynomial equation is a quadratic equation.

The zeros of a quadratic equation ax2+bx+c=0 can be found using the formula

  x=−b±b2−4ac2a

Applying above formula,

  ⇒x=−(−8)±(−8)2−4(8)(12)2(8)⇒x=8±64−38416⇒x=8±−32016⇒x=8±8−516⇒x=8±85i16⇒x=1±5i2⇒x=1+5i2,1−5i2

Conclusion:

Therefore, the zeros of given polynomial function are x=34,1+5i2 and 1−5i2.

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Chapter 2.5, Problem 66E
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Chapter 2.5, Problem 68E

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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