Use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. f(x) = x5 - 7x, between x = 1 and x = 2 Substitute x = 1 and into the function and simplify. X = 2 f(1) = f(2) = Interpret the results using the Intermediate Value Theorem. Because f is a polynomial function and since (1) is (negative and f(2) is positive there is at least one real zero between x = 1 and x = 2.

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
Section4.5: Zeros Of Polynomial Functions
Problem 80E
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Use the Intermediate Value Theorem to confirm that the given polynomial has at
least one zero within the given interval.
f(x) = x5 – 7x, between x = 1 and x = 2
Substitute x = 1 and x = 2 into the function and simplify.
f(1) =
f(2) =
Interpret the results using the Intermediate Value Theorem.
Because f is a polynomial function and since (1) is (negative
v and (2) is
there is at least one real zero between x = 1 and x = 2.
positive
Transcribed Image Text:Use the Intermediate Value Theorem to confirm that the given polynomial has at least one zero within the given interval. f(x) = x5 – 7x, between x = 1 and x = 2 Substitute x = 1 and x = 2 into the function and simplify. f(1) = f(2) = Interpret the results using the Intermediate Value Theorem. Because f is a polynomial function and since (1) is (negative v and (2) is there is at least one real zero between x = 1 and x = 2. positive
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