Consider the following equation. 3x4 - 8x3 + 5 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 – 8x3 + 5. The polynomial f is continuous on [2, 3], f(2) = Intermediate Value Theorem, there is a number c in (2, 3) such that f(c) = root in [2, 3]. < 0, and f(3) = In other words, the equation 3x4 - 8x3 + 5 = 0 has a > 0, so by the (b) Use Newton's method to approximate the root correct to six decimal places.

Consider the following equation. 3x4 - 8x3 + 5 = 0, [2, 3] (a) Explain how we know that the given equation must have a root in the given interval. Let f(x) = 3x4 – 8x3 + 5. The polynomial f is continuous on [2, 3], f(2) = Intermediate Value Theorem, there is a number c in (2, 3) such that f(c) = root in [2, 3]. < 0, and f(3) = In other words, the equation 3x4 - 8x3 + 5 = 0 has a > 0, so by the (b) Use Newton's method to approximate the root correct to six decimal places.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.3: Zeros Of Polynomials

Problem 65E

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