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1. Consider the problem of finding the roots of P(x) = (x – 1)(x – 3)(x – 5)(x –- 7)(x – 9)(x – 11)(x – 13)(x – 15)(x – 17)(x – 19). a. What are the roots of P(x)? :- b. If we define the perturbation P(x) = P(x) + 2x6, determine whether the problem of finding the roots of P(x) around the perturbation x6 an ill or well-conditioned problem.

1. Consider the problem of finding the roots of P(x) = (x – 1)(x – 3)(x – 5)(x –- 7)(x – 9)(x – 11)(x – 13)(x – 15)(x – 17)(x – 19). a. What are the roots of P(x)? :- b. If we define the perturbation P(x) = P(x) + 2x6, determine whether the problem of finding the roots of P(x) around the perturbation x6 an ill or well-conditioned problem.

Advanced Engineering Mathematics
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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1. Consider the problem of finding the roots of P(x) = (x – 1)(x – 3)(x – 5)(x – 7)(x – 9)(x – 11)(x – 13)(x – 15)(x – 17)(x – 19). a. What are the roots of P(x)? ; - b. If we define the perturbation P(x) = P(x) + 2x6, determine whether the problem of finding the roots of P(x) around the perturbation x6 an ill or well-conditioned problem.
Transcribed Image Text:1. Consider the problem of finding the roots of P(x) = (x – 1)(x – 3)(x – 5)(x – 7)(x – 9)(x – 11)(x – 13)(x – 15)(x – 17)(x – 19). a. What are the roots of P(x)? ; - b. If we define the perturbation P(x) = P(x) + 2x6, determine whether the problem of finding the roots of P(x) around the perturbation x6 an ill or well-conditioned problem.
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