53-56 - Polynomials with Specified Zeros Find a polynomial with real coefficients of the specified degree that satisfies the given conditions. 53. Degree 3; zeros -, 2, 3; constant coefficient 12 54. Degree 4; zeros 4 (multiplicity 2) and 3i; integer coefficients; coefficient of x² is -25 55. Complex Zeros of Polynomials Does there exist a polyno- mial of degree 4 with integer coefficients that has zeros i, 2i, 3i, and 4i? If so, find it. If not, explain why. 56. Polynomial with no Real Roots Prove that the equation 3x* + 5x² + 2 = 0 has no real root.
53-56 - Polynomials with Specified Zeros Find a polynomial with real coefficients of the specified degree that satisfies the given conditions. 53. Degree 3; zeros -, 2, 3; constant coefficient 12 54. Degree 4; zeros 4 (multiplicity 2) and 3i; integer coefficients; coefficient of x² is -25 55. Complex Zeros of Polynomials Does there exist a polyno- mial of degree 4 with integer coefficients that has zeros i, 2i, 3i, and 4i? If so, find it. If not, explain why. 56. Polynomial with no Real Roots Prove that the equation 3x* + 5x² + 2 = 0 has no real root.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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53–56 ■ Polynomials with Specified Zeros Find a polynomial
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given conditions.
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