EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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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 68E

a.

To determine

Verify the given factors of f(x) .

a.

Expert Solution
Check Mark

Answer to Problem 68E

  (2x+5)(5x−3)

  Verified

Explanation of Solution

Calculation:

Consider the following functions and factors of f(x)

  f(x)=10x3−11x2−72x+45 , (2x+5)(5x−3)

Divide the polynomial f(x)=10x3−11x2−72x+45 by (2x+5) using synthetic division,

  3/510−11−72456−34510−5−750

Since, the reminder is zero, so, (2x+5) is a factor of polynomial f(x)=10x3−11x2−72x+45 .

Again divide the polynomial f(x)=10x3−11x2−72x+45 by (5x−3) using synthetic division,

  −5/210−11−7245−2590−4510−36180

Since, the reminder is zero, so, (5x−3) is a factor of polynomial f(x)=10x3−11x2−72x+45 .

Hence, (2x+5) and (5x−3) is a factor of polynomial f(x)=10x3−11x2−72x+45 .

b.

To determine

Find the remaining factors of f(x) .

b.

Expert Solution
Check Mark

Answer to Problem 68E

  (x−3)

Explanation of Solution

Calculation:

From the above syntehtic division, rewrite the polynomial 10x3−11x2−72x+45 as

  f(x)=(5x−3)(10x2−5x−75)=(5x−3)(x−3)(10x+25)=5(5x−3)(x−3)(5x+5)

Hence, the remaining factors are (x−3) .

c.

To determine

Write the complete factorization of f(x) .

c.

Expert Solution
Check Mark

Answer to Problem 68E

  f(x)=5(5x−3)(x−3)(5x+5)

Explanation of Solution

Calculation:

Since, 5,(5x−3),,(x−3) and (5x+5) are factors of cubic polynomial 10x3−11x2−72x+45 .

Hence, the complete factorization of f(x) is given by f(x)=5(5x−3)(x−3)(5x+5) .

d.

To determine

List all real zeros of f .

d.

Expert Solution
Check Mark

Answer to Problem 68E

  35,3,−1

Explanation of Solution

Calculation:

To find all the zeros, put f(x)=0 and solve for x

  f(x)=05(5x−3)(x−3)(5x+5)=0

Set the first factor to zero and solve for x

  (5x−3)=0x=35

Set the second factor to zero and solve for x

  (x−3)=0x=3

Set the third factor to zero and solve for x

  (5x+5)=0x=−1

Hence, the zeros are given by 35,3,−1 .

e.

To determine

Graph a function.

e.

Expert Solution
Check Mark

Answer to Problem 68E

  EBK PRECALCULUS W/LIMITS, Chapter 2.3, Problem 68E , additional homework tip 1

Explanation of Solution

Calculation:

Using graphical utility to graph the function f(x)=10x3−11x2−72x+45 is given as,

  EBK PRECALCULUS W/LIMITS, Chapter 2.3, Problem 68E , additional homework tip 2

Hence, the graph is shown above.

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Chapter 2.3, Problem 67E
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Chapter 2.3, Problem 69E

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

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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 - 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. 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. 1PSCh. 2 - Prob. 2PSCh. 2 - Prob. 3PSCh. 2 - Prob. 4PSCh. 2 - Prob. 5PSCh. 2 - Prob. 6PSCh. 2 - Prob. 7PSCh. 2 - Prob. 8PSCh. 2 - Prob. 9PSCh. 2 - Prob. 10PSCh. 2 - Prob. 11PSCh. 2 - Prob. 12PSCh. 2 - Prob. 13PS
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