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
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Chapter 5.4, Problem 28WE

a.

To determine

To find the domain of the given rational function.

a.

Expert Solution
Check Mark

Answer to Problem 28WE

Domain: (,1)(1,)

Explanation of Solution

Given:

Rational function: h(t)=t3+4t2t4t3t2+t1

Concept used:

To find the domain of the rational function, the following steps are to be followed:

  1. Equate the denominator equal to zero.
  2. Solve and find the t values that make the denominator equal to zero.
  3. The domain is all the real numbers except for those t values equal to zero.

Calculation:

The given rational function is h(t)=t3+4t2t4t3t2+t1

The denominator of the given function is t3t2+t1.

Equating the denominator to zero,

  t3t2+t1=0

Grouping the terms,

  (t3t2)+(t1)=0t2(t1)+(t1)=0(t2+1)(t1)=0(t2+1)and(t1)=0

When (t2+1)=0,

Subtracting 1 on both sides,

  t2+11=01t2=1

Taking square root on both sides,

  t2=1t=±i

When (t1)=0,

Adding 1 on both sides,

  t1+1=0+1t=1

Imaginary roots cannot be plotted on real plane.

Hence, the domain of the function is all real numbers except t=1 .

Conclusion:

Therefore, the domain of the function is a (,1)(1,).

b.

To determine

To find the zeros of the function if any.

b.

Expert Solution
Check Mark

Answer to Problem 28WE

  t=4t=±1

Explanation of Solution

Given:

Rational function: h(t)=t3+4t2t4t3t2+t1

Concept used:

To find the zeros of the rational function,

  1. Equate h(t)=0.
  2. Simplify and find the values of t which are the zeros of the rational function.

Calculation:

Equate the rational function h(t) to zero.

  h(t)=0t3+4t2t4t3t2+t1=0

Cross multiplying,

  t3+4t2t4=(t3t2+t1)(0)t3+4t2t4=0

Grouping the terms,

  t3+4t2t4=0t2(t+4)(t+4)=0(t21)(t+4)=0(t21)and(t+4)=0

When (t21)=0,

Adding 1 on both sides,

  t21+1=0+1t2=1

Taking square root on both sides,

  t2=1t=±1

When (t+4)=0,

Subtracting4 on both sides,

  t+44=04t=4

Conclusion:

Therefore, the zeroes of the rational function are t=4 and t=±1 .

Chapter 5 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 5.1 - Prob. 11OECh. 5.1 - Prob. 12OECh. 5.1 - Prob. 1WECh. 5.1 - Prob. 2WECh. 5.1 - Prob. 3WECh. 5.1 - Prob. 4WECh. 5.1 - Prob. 5WECh. 5.1 - Prob. 6WECh. 5.1 - Prob. 7WECh. 5.1 - Prob. 8WECh. 5.1 - Prob. 9WECh. 5.1 - Prob. 10WECh. 5.1 - Prob. 11WECh. 5.1 - Prob. 12WECh. 5.1 - Prob. 13WECh. 5.1 - Prob. 14WECh. 5.1 - Prob. 15WECh. 5.1 - Prob. 16WECh. 5.1 - Prob. 17WECh. 5.1 - Prob. 18WECh. 5.1 - Prob. 19WECh. 5.1 - Prob. 20WECh. 5.1 - Prob. 21WECh. 5.1 - Prob. 22WECh. 5.1 - Prob. 23WECh. 5.1 - Prob. 24WECh. 5.1 - Prob. 25WECh. 5.1 - Prob. 26WECh. 5.1 - Prob. 27WECh. 5.1 - Prob. 28WECh. 5.1 - Prob. 29WECh. 5.1 - Prob. 30WECh. 5.1 - Prob. 31WECh. 5.1 - Prob. 32WECh. 5.1 - Prob. 33WECh. 5.1 - Prob. 34WECh. 5.1 - Prob. 35WECh. 5.1 - Prob. 36WECh. 5.1 - Prob. 1MRECh. 5.1 - Prob. 2MRECh. 5.1 - Prob. 3MRECh. 5.1 - Prob. 4MRECh. 5.1 - Prob. 5MRECh. 5.1 - Prob. 6MRECh. 5.1 - Prob. 7MRECh. 5.1 - Prob. 8MRECh. 5.1 - Prob. 9MRECh. 5.1 - Prob. 10MRECh. 5.1 - Prob. 11MRECh. 5.1 - Prob. 12MRECh. 5.1 - 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