1 f(x) = 3x³ − x² + 27x − 9, - -
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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Question

Transcribed Image Text:# Polynomial Root Analysis
## Given \( f(x) = 3x^3 - x^2 + 27x - 9 \),
**a) Determine the maximum number of real roots.**
____________
**b) How many possible positive roots?**
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**c) How many possible negative roots?**
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**d) List all possible rational roots.**
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**e) Find and list each real and complex root with its multiplicity.**
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**f) List the polynomial as a product of linear factors.**
_____________________________________________________
**g) Determine where the graph touches the x-axis and where it crosses the x-axis. Explain the answer.**
_____________________________________________________
_____________________________________________________
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