The Fundamental Theorem of Algebra Section 4.4 361 33. r(x)= x* +7x' – 41x² +33x 34. d(x)= x° –x* – 18x' +18x² +81x–81 35. P(x)= x³ -6x² +28x- 40 36. g(x)= x° –x* – 16x² +16 %3D Construct polynomial functions with the stated properties. See Example 3. of 37. Third-degree, only real coefficients, 42. Fifth-degree, -2 is -1 and 5+i are two of the zeros, zero multiplicity 2, another integer is a zero of multiplicity 3, y-intercept is 108, leading coefficient is 1. y-intercept is -52. 38. Fourth-degree, only real coefficients, 7 and i5 are two of the zeros, y-intercept is -35. 43. Third-degree, only real coefficients, -4 and 3+i are two of the zeros, y-intercept is -40. 39. Fifth-degree, 1 is a zero of multiplicity 3,-2 is the only other zero, leading 44. Fifth-degree, 1 is a zero of multiplicity 4, -2 is the only other zero, leading coefficient is 2. coefficient is 4. 40. Fifth-degree, only real coefficients, 0 is the only real zero, 1+i is a zero of 45. Third-degree, only real coefficients, multiplicity 1, leading coefficient is 1. -4 and 4+i are two of the zeros, y-intercept is -68. 41. Fourth-degree, only real coefficients, x-intercepts are 0 and 6,-2i is a zero, leading coefficient is 3.
The Fundamental Theorem of Algebra Section 4.4 361 33. r(x)= x* +7x' – 41x² +33x 34. d(x)= x° –x* – 18x' +18x² +81x–81 35. P(x)= x³ -6x² +28x- 40 36. g(x)= x° –x* – 16x² +16 %3D Construct polynomial functions with the stated properties. See Example 3. of 37. Third-degree, only real coefficients, 42. Fifth-degree, -2 is -1 and 5+i are two of the zeros, zero multiplicity 2, another integer is a zero of multiplicity 3, y-intercept is 108, leading coefficient is 1. y-intercept is -52. 38. Fourth-degree, only real coefficients, 7 and i5 are two of the zeros, y-intercept is -35. 43. Third-degree, only real coefficients, -4 and 3+i are two of the zeros, y-intercept is -40. 39. Fifth-degree, 1 is a zero of multiplicity 3,-2 is the only other zero, leading 44. Fifth-degree, 1 is a zero of multiplicity 4, -2 is the only other zero, leading coefficient is 2. coefficient is 4. 40. Fifth-degree, only real coefficients, 0 is the only real zero, 1+i is a zero of 45. Third-degree, only real coefficients, multiplicity 1, leading coefficient is 1. -4 and 4+i are two of the zeros, y-intercept is -68. 41. Fourth-degree, only real coefficients, x-intercepts are 0 and 6,-2i is a zero, leading coefficient is 3.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 4E
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Transcribed Image Text:The Fundamental Theorem of Algebra Section 4.4
361
33. r(x)= x* +7x' – 41x² +33x
34. d(x)= x° –x* – 18x' +18x² +81x–81
35. P(x)= x³ -6x² +28x- 40
36. g(x)= x° –x* – 16x² +16
%3D
Construct polynomial functions with the stated properties. See Example 3.
of
37. Third-degree, only real coefficients, 42. Fifth-degree, -2 is
-1 and 5+i are two of the zeros,
zero
multiplicity 2, another integer is a
zero of multiplicity 3, y-intercept is
108, leading coefficient is 1.
y-intercept is -52.
38. Fourth-degree, only real coefficients,
7 and i5 are two of the zeros,
y-intercept is -35.
43. Third-degree, only real coefficients,
-4 and 3+i are two of the zeros,
y-intercept is -40.
39. Fifth-degree, 1 is a zero of multiplicity
3,-2 is the only other zero, leading 44. Fifth-degree, 1 is a zero of multiplicity
4, -2 is the only other zero, leading
coefficient is 2.
coefficient is 4.
40. Fifth-degree, only real coefficients, 0
is the only real zero, 1+i is a zero of 45. Third-degree, only real coefficients,
multiplicity 1, leading coefficient is 1.
-4 and 4+i are two of the zeros,
y-intercept is -68.
41. Fourth-degree, only real coefficients,
x-intercepts are 0 and 6,-2i is a zero,
leading coefficient is 3.
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