Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015
1st Edition
ISBN: 9781680331165
Author: HOUGHTON MIFFLIN HARCOURT
Publisher: Houghton Mifflin Harcourt
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Chapter 4.6, Problem 14E
To determine

To find: all zeros of the polynomial function.

Expert Solution & Answer
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Answer to Problem 14E

The zeros are 1,2 and 3i,3i .

Explanation of Solution

Given information:

Given function,

  h(x)=x4x3+7x29x18

Calculation:

Consider the equation h(x)=x4x3+7x29x18 :

Because h(x) is a polynomial function of degree 4, so it has 4 zeros.

The possible rational zeros are ±1,±2,±3,±6,±9and±18.

Choose reasonable values from the list above to test using the graph of the function.

  Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015, Chapter 4.6, Problem 14E

From the above graph the values are x=1andx=2 .

Test out the binomial using synthetic division until a zero is found.

  111791812918129180

Factor out the binomial using the result of above synthetic division.

  h(x)=x4x3+7x29x18=(x+1)(x32x2+9x18)

Repeat the steps above for f(x)=x32x2+9x18 .

The possible rational are ±1,±2,±3,±6,±9and±18. Test the value using synthetic division until a zero is found.

  21291820181090

Factor out the binomial using the result of above synthetic division.

  h(x)=(x+1)(x32x2+9x18)=(x+1)(x2)(x2+9)

Solve h(x)=0 .

  (x+1)(x2)(x2+9)=0x+1=0orx2=0orx2+9=0x=1orx=3orx2+9=0

Now solve the equation x2+9=0

  x2=9x=±9x=±3i

Therefore, the zeros are 1,2 and 3i,3i .

Chapter 4 Solutions

Big Ideas Math A Bridge To Success Algebra 2: Student Edition 2015

Ch. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 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. 4.2 - Prob. 1ECh. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Prob. 4ECh. 4.2 - Prob. 5ECh. 4.2 - Prob. 6ECh. 4.2 - Prob. 7ECh. 4.2 - 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