Polynomial and Rational Functions CHAPTER 3 294 37-46 - Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that satisfies the given conditions. 37. P has degree 2 and zeros 1 + i and 1 -i. – ¡V2. 38. P has degree 2 and zeros 1 + iV2 and 1 39. Q has degree 3 and zeros 3, 2i, and –2i. 40. Q has degree 3 and zeros 0 and i. .41. P has degree 3 and zeros 2 and i. 42. Q has degree 3 and zeros –3 and 1 + i. 43. R has degree 4 and zeros 1 - 2i and 1, with 1 a zero of multiplicity 2. 44. S has degree 4 and zeros 2i and 3i. 45. T has degree 4, zeros i and 1 + i, and constant term 12. 46. U has degree 5, zeros , –1, and -i, and leading coefficient 4; the zero -1 has multiplicity 2. 2 47–64 - Finding Complex Zeros polynomial. Find all zeros of the 47. P(x) = x³ + 2x? + 4x + 8 %3D 48. P(x) = x³ – 7x² + 17x – 15 49. P(x) = x³ - 2x2 + 2x - 1 50. P(x) = x³ + 7x2 + 18x + 18 51. P(x) = x³ - 3x2 + 3x – 2

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter3: Polynomial And Rational Functions
Section3.5: Complex Zeros And The Fundamental Theorem Of Algebra
Problem 46E: Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that satisfies...
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Polynomial and Rational Functions
CHAPTER 3
294
37-46 - Finding a Polynomial with Specified Zeros Find a
polynomial with integer coefficients that satisfies the given
conditions.
37. P has degree 2 and zeros 1 + i and 1 -i.
– ¡V2.
38. P has degree 2 and zeros 1 + iV2 and 1
39. Q has degree 3 and zeros 3, 2i, and –2i.
40. Q has degree 3 and zeros 0 and i.
.41. P has degree 3 and zeros 2 and i.
42. Q has degree 3 and zeros –3 and 1 + i.
43. R has degree 4 and zeros 1 - 2i and 1, with 1 a zero of
multiplicity 2.
44. S has degree 4 and zeros 2i and 3i.
45. T has degree 4, zeros i and 1 + i, and constant term 12.
46. U has degree 5, zeros , –1, and -i, and leading coefficient
4; the zero -1 has multiplicity 2.
2
47–64 - Finding Complex Zeros
polynomial.
Find all zeros of the
47. P(x) = x³ + 2x? + 4x + 8
%3D
48. P(x) = x³ – 7x² + 17x – 15
49. P(x) = x³ - 2x2 + 2x - 1
50. P(x) = x³ + 7x2 + 18x + 18
51. P(x) = x³ - 3x2 + 3x – 2
Transcribed Image Text:Polynomial and Rational Functions CHAPTER 3 294 37-46 - Finding a Polynomial with Specified Zeros Find a polynomial with integer coefficients that satisfies the given conditions. 37. P has degree 2 and zeros 1 + i and 1 -i. – ¡V2. 38. P has degree 2 and zeros 1 + iV2 and 1 39. Q has degree 3 and zeros 3, 2i, and –2i. 40. Q has degree 3 and zeros 0 and i. .41. P has degree 3 and zeros 2 and i. 42. Q has degree 3 and zeros –3 and 1 + i. 43. R has degree 4 and zeros 1 - 2i and 1, with 1 a zero of multiplicity 2. 44. S has degree 4 and zeros 2i and 3i. 45. T has degree 4, zeros i and 1 + i, and constant term 12. 46. U has degree 5, zeros , –1, and -i, and leading coefficient 4; the zero -1 has multiplicity 2. 2 47–64 - Finding Complex Zeros polynomial. Find all zeros of the 47. P(x) = x³ + 2x? + 4x + 8 %3D 48. P(x) = x³ – 7x² + 17x – 15 49. P(x) = x³ - 2x2 + 2x - 1 50. P(x) = x³ + 7x2 + 18x + 18 51. P(x) = x³ - 3x2 + 3x – 2
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