Find a polynomial f(x) of degree 5 that has the following zeros. -6, 1, 8, 4, -2 Leave your answer in factored form.
Find a polynomial f(x) of degree 5 that has the following zeros. -6, 1, 8, 4, -2 Leave your answer in factored form.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Polynomial Function with Given Zeros
**Problem Statement:**
Find a polynomial \( f(x) \) of degree 5 that has the following zeros.
\[ -6, \, 1, \, 8, \, 4, \, -2 \]
Leave your answer in factored form.
**Solution:**
To write a polynomial function in factored form given its zeros:
- Each zero \( a \) of the polynomial will correspond to a factor of \( (x - a) \).
Given the zeros \(-6, \, 1, \, 8, \, 4, \, -2\), the polynomial can be written as:
\[ f(x) = (x + 6)(x - 1)(x - 8)(x - 4)(x + 2) \]
Thus, the polynomial \( f(x) \) in factored form is:
\[ f(x) = (x + 6)(x - 1)(x - 8)(x - 4)(x + 2) \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbae73a37-719e-4892-8745-1f816a181ea7%2Fcee1aafb-3387-464b-8708-5c63023d771c%2Filsbk5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Polynomial Function with Given Zeros
**Problem Statement:**
Find a polynomial \( f(x) \) of degree 5 that has the following zeros.
\[ -6, \, 1, \, 8, \, 4, \, -2 \]
Leave your answer in factored form.
**Solution:**
To write a polynomial function in factored form given its zeros:
- Each zero \( a \) of the polynomial will correspond to a factor of \( (x - a) \).
Given the zeros \(-6, \, 1, \, 8, \, 4, \, -2\), the polynomial can be written as:
\[ f(x) = (x + 6)(x - 1)(x - 8)(x - 4)(x + 2) \]
Thus, the polynomial \( f(x) \) in factored form is:
\[ f(x) = (x + 6)(x - 1)(x - 8)(x - 4)(x + 2) \]
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