Explanation Given: The zeros of the polynomial function with rational coefficients are − 4 i and 5 . Concept: The two concept is used here which is given below, a) According to the fundamental theorem of algebra, every polynomial function of degree n can be factorized into n linear factor, where n ≥ 1 and factor are not necessarily unique. f ( x ) = a n ( x − c 1 ) ( x − c 2 ) ....... ( x − c n ) b) If the polynomial function has rational coefficient then, complex zeros occur in a con jugate pair. Suppose the polynomial function has rational coefficient with p + i q is zero of polynomial function where p and q is rational then, the conjugate of p + i q is also a zero of a polynomial function. Calculation: The given zeros of the polynomial function are − 4 i and 5 . In the given zeros, one zero of the polynomial function is complex then, conjugate of the complex number is also a zero of the polynomial function. The other zero of the polynomial function is 4 i . Thus, the lowest degree of the polynomial function is 3. Let f ( x ) be the polynomial function of lowest degree 3. The factor of the polynomial function f ( x ) is x + 4 i , x − 5 and x − 4 i . According to the fundamental theorem of algebra, the function f ( x ) can be written as, f ( x ) = a 3 ( x + 4 i ) ( x − 5 ) ( x − 4 i ) The number a 3 is any nonzero number

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ISBN: 9780321969576

Author: Judith A. Beecher, Judith A. Penna, Marvin L. Bittinger

Publisher: PEARSON

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Chapter 4.4, Problem 37E

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The polynomial function of lowest degree with rational coefficients that has the number of zeros as −4i, 5.

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Chapter 4.4, Problem 36E

Chapter 4.4, Problem 38E

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Chapter 4 Solutions

College Algebra (5th Edition)

Ch. 4.1 - Determine the leading term, the leading...Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E

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The polynomial function of lowest degree with rational coefficients that has the number of zeros as − 4 i , 5 .

To find: The polynomial function of lowest degree with rational coefficients that has the number of zeros as −4i, 5.

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Chapter 4 Solutions

To find:

The polynomial function of lowest degree with rational coefficients that has the number of zeros as −4i, 5.