Glencoe Algebra 2 Student Edition C2014
Glencoe Algebra 2 Student Edition C2014
1st Edition
ISBN: 9780076639908
Author: McGraw-Hill Glencoe
Publisher: MCG
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Chapter SH, Problem 5.20EP
To determine

Find the zeros of the given function.

Expert Solution & Answer
Check Mark

Answer to Problem 5.20EP

The function has zeros at 1,1,2i and 2i .

Explanation of Solution

Given:

The given function is f(x)=x4+3x24 .

Calculation:

Since f(x) has degree 4 , the function has 4 zeros.

Find the type of zeros.

Examine the number of sign changes for f(x) and f(x) .

  f(x)=x4+3x24noyes

Because there are one sign changes for the coefficients of f(x) , the function has one or zero positive real zeros.

  f(x)=(x)4+3(x)24=x4+3x24noyes

Because there is one sign changes for the coefficients of f(x) , the function has one or zero negative real zeros.

Thus, f(x) has two real zerosand two imaginary zeros or four imaginary zeros.

Determine the real zeros. List some possible values, and then use synthetic substitution to evaluate f(x) for real values of x .

    x10304
    21271424
    111440
    010304
    111440
    21271424

From the table, zero occurs at x=1 and x=1 . Since there are one negative real zero and one positive real zeros.

Use synthetic substitution with depressed polynomial f(x)=x3+x2+4x+4 to find two imaginary zeros.

Substitute f(x)=0 .

  x3+x2+4x+4=0

Use factorization method.

  x3+x2+4x+4=0x2(x+1)+4(x+1)=0(x+1)(x2+4)=0x2+4=0x2=4x=±4i2=1x=±22i2x=±2i

Hence the function haszeros at 1,1,2i and 2i .

Chapter SH Solutions

Glencoe Algebra 2 Student Edition C2014

Ch. SH - Prob. 1.11EPCh. SH - Prob. 1.12EPCh. SH - Prob. 1.13EPCh. SH - Prob. 1.14EPCh. SH - Prob. 1.15EPCh. SH - Prob. 1.16EPCh. SH - Prob. 1.17EPCh. SH - Prob. 1.18EPCh. SH - Prob. 1.19EPCh. SH - Prob. 1.20EPCh. SH - Prob. 1.21EPCh. SH - Prob. 1.22EPCh. SH - Prob. 1.23EPCh. SH - Prob. 1.24EPCh. SH - Prob. 1.25EPCh. SH - Prob. 2.1EPCh. SH - Prob. 2.2EPCh. SH - Prob. 2.3EPCh. SH - Prob. 2.4EPCh. SH - Prob. 2.5EPCh. SH - Prob. 2.6EPCh. SH - Prob. 2.7EPCh. SH - Prob. 2.8EPCh. SH - Prob. 2.9EPCh. SH - Prob. 2.10EPCh. SH - Prob. 2.11EPCh. SH - Prob. 2.12EPCh. SH - Prob. 2.13EPCh. SH - Prob. 2.14EPCh. SH - Prob. 2.15EPCh. SH - Prob. 2.16EPCh. SH - Prob. 2.17EPCh. SH - Prob. 2.18EPCh. SH - Prob. 2.19EPCh. SH - Prob. 2.20EPCh. SH - Prob. 2.21EPCh. SH - Prob. 2.22EPCh. SH - Prob. 2.23EPCh. SH - Prob. 2.24EPCh. SH - Prob. 2.25EPCh. SH - Prob. 3.1EPCh. SH - Prob. 3.2EPCh. SH - Prob. 3.3EPCh. SH - Prob. 3.4EPCh. SH - Prob. 3.5EPCh. SH - Prob. 3.6EPCh. SH - Prob. 3.7EPCh. SH - Prob. 3.8EPCh. SH - Prob. 3.9EPCh. SH - Prob. 3.10EPCh. SH - Prob. 3.11EPCh. SH - Prob. 3.12EPCh. SH - Prob. 3.13EPCh. SH - Prob. 3.14EPCh. SH - Prob. 3.15EPCh. SH - Prob. 3.16EPCh. SH - Prob. 3.17EPCh. SH - Prob. 3.18EPCh. SH - Prob. 3.19EPCh. SH - Prob. 3.20EPCh. SH - Prob. 3.21EPCh. SH - Prob. 3.22EPCh. SH - Prob. 3.23EPCh. SH - Prob. 3.24EPCh. SH - Prob. 3.25EPCh. SH - Prob. 3.26EPCh. SH - Prob. 4.1EPCh. SH - Prob. 4.2EPCh. SH - Prob. 4.3EPCh. SH - Prob. 4.4EPCh. SH - Prob. 4.5EPCh. SH - Prob. 4.6EPCh. SH - Prob. 4.7EPCh. SH - Prob. 4.8EPCh. SH - Prob. 4.9EPCh. SH - Prob. 4.10EPCh. SH - Prob. 4.11EPCh. SH - Prob. 4.12EPCh. SH - Prob. 4.13EPCh. SH - Prob. 4.14EPCh. SH - Prob. 4.15EPCh. SH - Prob. 4.16EPCh. SH - Prob. 4.17EPCh. SH - Prob. 4.18EPCh. SH - Prob. 4.19EPCh. SH - Prob. 4.20EPCh. SH - Prob. 4.21EPCh. SH - Prob. 4.22EPCh. SH - Prob. 4.23EPCh. SH - Prob. 4.24EPCh. SH - Prob. 4.25EPCh. SH - Prob. 5.1EPCh. SH - Prob. 5.2EPCh. SH - Prob. 5.3EPCh. SH - Prob. 5.4EPCh. SH - Prob. 5.5EPCh. SH - Prob. 5.6EPCh. SH - Prob. 5.7EPCh. SH - Prob. 5.8EPCh. SH - Prob. 5.9EPCh. SH - Prob. 5.10EPCh. SH - Prob. 5.11EPCh. SH - Prob. 5.12EPCh. SH - Prob. 5.13EPCh. SH - Prob. 5.14EPCh. SH - Prob. 5.15EPCh. SH - Prob. 5.16EPCh. SH - Prob. 5.17EPCh. SH - Prob. 5.18EPCh. SH - Prob. 5.19EPCh. SH - Prob. 5.20EPCh. SH - Prob. 5.21EPCh. SH - Prob. 5.22EPCh. SH - Prob. 5.23EPCh. SH - Prob. 5.24EPCh. SH - Prob. 5.25EPCh. SH - Prob. 6.1EPCh. SH - Prob. 6.2EPCh. SH - Prob. 6.3EPCh. SH - Prob. 6.4EPCh. SH - Prob. 6.5EPCh. SH - Prob. 6.6EPCh. SH - Prob. 6.7EPCh. SH - Prob. 6.8EPCh. SH - Prob. 6.9EPCh. SH - Prob. 6.10EPCh. SH - Prob. 6.11EPCh. SH - Prob. 6.12EPCh. SH - Prob. 6.13EPCh. SH - Prob. 6.14EPCh. SH - Prob. 6.15EPCh. SH - Prob. 6.16EPCh. SH - Prob. 6.17EPCh. SH - Prob. 6.18EPCh. SH - Prob. 6.19EPCh. SH - Prob. 6.20EPCh. SH - Prob. 6.21EPCh. SH - Prob. 6.22EPCh. SH - Prob. 6.23EPCh. SH - Prob. 6.24EPCh. SH - Prob. 6.25EPCh. SH - Prob. 7.1EPCh. SH - Prob. 7.2EPCh. SH - Prob. 7.3EPCh. SH - Prob. 7.4EPCh. SH - Prob. 7.5EPCh. SH - Prob. 7.6EPCh. SH - Prob. 7.7EPCh. SH - Prob. 7.8EPCh. SH - Prob. 7.9EPCh. SH - Prob. 7.10EPCh. SH - Prob. 7.11EPCh. SH - Prob. 7.12EPCh. SH - Prob. 7.13EPCh. SH - Prob. 7.14EPCh. SH - Prob. 7.15EPCh. SH - Prob. 7.16EPCh. SH - Prob. 7.17EPCh. SH - Prob. 7.18EPCh. SH - Prob. 7.19EPCh. SH - Prob. 7.20EPCh. SH - Prob. 7.21EPCh. SH - Prob. 7.22EPCh. SH - Prob. 7.23EPCh. SH - Prob. 7.24EPCh. SH - Prob. 7.25EPCh. SH - Prob. 8.1EPCh. SH - Prob. 8.2EPCh. SH - Prob. 8.3EPCh. SH - Prob. 8.4EPCh. SH - Prob. 8.5EPCh. SH - Prob. 8.6EPCh. SH - Prob. 8.7EPCh. SH - Prob. 8.8EPCh. SH - Prob. 8.9EPCh. SH - Prob. 8.10EPCh. SH - Prob. 8.11EPCh. SH - Prob. 8.12EPCh. SH - Prob. 8.13EPCh. SH - Prob. 8.14EPCh. SH - Prob. 8.15EPCh. SH - Prob. 8.16EPCh. SH - Prob. 8.17EPCh. SH - Prob. 8.18EPCh. SH - Prob. 8.19EPCh. SH - Prob. 9.1EPCh. SH - Prob. 9.2EPCh. SH - Prob. 9.3EPCh. SH - Prob. 9.4EPCh. SH - Prob. 9.5EPCh. SH - Prob. 9.6EPCh. SH - Prob. 9.7EPCh. SH - Prob. 9.8EPCh. SH - Prob. 9.9EPCh. SH - Prob. 9.10EPCh. SH - Prob. 9.11EPCh. SH - Prob. 9.12EPCh. SH - Prob. 9.13EPCh. SH - Prob. 9.14EPCh. SH - Prob. 9.15EPCh. SH - Prob. 9.16EPCh. SH - Prob. 9.17EPCh. SH - Prob. 9.18EPCh. SH - Prob. 9.19EPCh. SH - Prob. 9.20EPCh. SH - Prob. 9.21EPCh. SH - Prob. 10.1EPCh. SH - Prob. 10.2EPCh. SH - Prob. 10.3EPCh. SH - Prob. 10.4EPCh. SH - Prob. 10.5EPCh. SH - Prob. 10.6EPCh. SH - Prob. 10.7EPCh. SH - Prob. 10.8EPCh. SH - Prob. 10.9EPCh. SH - Prob. 10.10EPCh. SH - Prob. 10.11EPCh. SH - Prob. 10.12EPCh. SH - Prob. 10.13EPCh. SH - Prob. 10.14EPCh. SH - Prob. 10.15EPCh. SH - Prob. 10.16EPCh. SH - Prob. 10.17EPCh. SH - Prob. 10.18EPCh. SH - Prob. 10.19EPCh. SH - Prob. 10.20EPCh. SH - Prob. 10.21EPCh. SH - Prob. 10.22EPCh. SH - Prob. 10.23EPCh. SH - Prob. 10.24EPCh. SH - Prob. 10.25EPCh. SH - Prob. 10.26EPCh. SH - Prob. 11.1EPCh. SH - Prob. 11.2EPCh. SH - Prob. 11.3EPCh. SH - Prob. 11.4EPCh. SH - Prob. 11.5EPCh. SH - Prob. 11.6EPCh. SH - Prob. 11.7EPCh. SH - Prob. 11.8EPCh. SH - Prob. 11.9EPCh. SH - Prob. 11.10EPCh. SH - Prob. 11.11EPCh. SH - Prob. 11.12EPCh. SH - Prob. 11.13EPCh. SH - Prob. 11.14EPCh. SH - Prob. 12.1EPCh. SH - Prob. 12.2EPCh. SH - Prob. 12.3EPCh. SH - Prob. 12.4EPCh. SH - Prob. 12.5EPCh. SH - Prob. 12.6EPCh. SH - Prob. 12.7EPCh. SH - Prob. 12.8EPCh. SH - Prob. 12.9EPCh. SH - Prob. 12.10EPCh. SH - Prob. 12.11EPCh. SH - Prob. 12.12EPCh. SH - Prob. 12.13EPCh. SH - Prob. 12.14EPCh. SH - Prob. 12.15EPCh. SH - Prob. 12.16EPCh. SH - Prob. 12.17EPCh. SH - Prob. 12.18EPCh. SH - Prob. 12.19EPCh. SH - Prob. 12.20EPCh. SH - Prob. 12.21EPCh. SH - Prob. 12.22EPCh. SH - Prob. 12.23EPCh. SH - Prob. 12.24EPCh. SH - Prob. 13.1EPCh. SH - Prob. 13.2EPCh. SH - Prob. 13.3EPCh. SH - Prob. 13.4EPCh. SH - Prob. 13.5EPCh. SH - Prob. 13.6EPCh. SH - Prob. 13.7EPCh. SH - Prob. 13.8EPCh. SH - Prob. 13.9EPCh. SH - Prob. 13.10EPCh. SH - Prob. 13.11EPCh. SH - Prob. 13.12EPCh. SH - Prob. 13.13EPCh. SH - Prob. 13.14EPCh. SH - Prob. 13.15EPCh. SH - Prob. 13.16EPCh. SH - Prob. 13.17EPCh. SH - Prob. 13.18EPCh. SH - Prob. 13.19EPCh. SH - Prob. 13.20EPCh. SH - Prob. 13.21EPCh. SH - Prob. 13.22EP
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