Math Problem Statement
Use the Intermediate Value Theorem to show that there is a root of the given equation in the specified interval. x4 + x − 5 = 0, (1, 2) f(x) = x4 + x − 5 is defined on the closed interval [1, 2], f(1) = -3 , and f(2) = 13 . Since −3 < __< 13, there is a number c in (1, 2) such that f(c) = 𝜀 by the Intermediate Value Theorem. Thus, there is a root of the equation x4 + x − 5 = 0 in the interval (1, 2)
Solution
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Math Problem Analysis
Mathematical Concepts
Polynomials
Roots of Equations
Continuity
Formulas
f(x) = x^4 + x - 5
Theorems
Intermediate Value Theorem
Suitable Grade Level
Grades 11-12
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