Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 3-i, √5 The polynomial function in expanded form is f(x) =
Find a polynomial function of lowest degree with rational coefficients that has the given numbers as some of its zeros. 3-i, √5 The polynomial function in expanded form is f(x) =
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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![**Problem Statement:**
Find a polynomial function of the lowest degree with rational coefficients that has the given numbers as some of its zeros:
\(3 - i, \sqrt{5}\)
**Solution:**
The polynomial function in expanded form is \( f(x) = \) [Input box or field for solution].
*Explanation:*
- To find a polynomial with rational coefficients containing these zeros, remember that complex and irrational roots appear in conjugate pairs. Consequently, if \(3-i\) is a root, \(3+i\) is also a root. Similarly, if \(\sqrt{5}\) is a root, \(-\sqrt{5}\) is also a root.
- Construct the polynomial using these roots and expand to attain a polynomial with rational coefficients.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdf429993-eecf-4773-959c-7bbde76a8695%2Fc4f47e47-6c7d-4fa4-8409-04388874416c%2Fy3v5qag_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Find a polynomial function of the lowest degree with rational coefficients that has the given numbers as some of its zeros:
\(3 - i, \sqrt{5}\)
**Solution:**
The polynomial function in expanded form is \( f(x) = \) [Input box or field for solution].
*Explanation:*
- To find a polynomial with rational coefficients containing these zeros, remember that complex and irrational roots appear in conjugate pairs. Consequently, if \(3-i\) is a root, \(3+i\) is also a root. Similarly, if \(\sqrt{5}\) is a root, \(-\sqrt{5}\) is also a root.
- Construct the polynomial using these roots and expand to attain a polynomial with rational coefficients.
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