sufficiently large c Use the intermediate value theorem to prove that any polynomial function of odd degree with realcoefficients has at least one real root. Hint: Show that if P is a polynomial function of odd degree thenfor sufficiently large c, P(c)P(-c) < 0.

Intermediate Value theorem: If f is a function which is continuous at every point of the interval…

Answered: Use the intermediate value theorem to…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter4: Polynomial And Rational Functions

Section4.CR: Chapter Review

Problem 30E

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Use the intermediate value theorem to prove that any polynomial function of odd degree with real coefficients has at least one real root. Hint: Show that if P is a polynomial function of odd degree then for sufficiently large c, P(c)P(-c) < 0.