Caleb was determining the nature of the roots of the polynomial equation x* + 2x° +x +1 = 0. Follow Caleb's work below and identify his mistake. Then explain WHY it is wrong and show/tell Caleb how to correctly find the nature of the roots. Caleb's work/explanation: P(x) = x* + 2x +x +1 has 0 sign changes. P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes. Since there are no sign changes for P(x), there are no positive roots. Since there are no sign changes for P(-x), there are no negative roots. Since none of the roots are positive or negative, all four roots must be complex.
Caleb was determining the nature of the roots of the polynomial equation x* + 2x° +x +1 = 0. Follow Caleb's work below and identify his mistake. Then explain WHY it is wrong and show/tell Caleb how to correctly find the nature of the roots. Caleb's work/explanation: P(x) = x* + 2x +x +1 has 0 sign changes. P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes. Since there are no sign changes for P(x), there are no positive roots. Since there are no sign changes for P(-x), there are no negative roots. Since none of the roots are positive or negative, all four roots must be complex.
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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Transcribed Image Text:Caleb was determining the nature of the roots of the
2
polynomial equation x* + 2x° + x +1 = 0.
Follow Caleb's work below and identify his mistake.
Then explain WHY it is wrong and show/tell Caleb how
to correctly find the nature of the roots.
Caleb's work/explanation:
P(x) = x* + 2x +x +1 has 0 sign changes.
P(-x) = -x* - 2r° – x2 – 1 has 0 sign changes.
Since there are no sign changes for P(x), there are no
positive roots.
Since there are no sign changes for P(-x), there are
no negative roots.
Since none of the roots are positive or negative, all four
roots must be complex.
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