Answered: (a) By sketching the graph of the… | bartleby

Algebra & Trigonometry with Analytic Geometry

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 14T

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Question

Consider the equation x^3 + x^2 - 1 = 0

(a) By sketching the graph of the function f(x) = x³ + x² – 1, show that
the equation f(x) = 0 has only one real root.
(b) Show that the real root of f(x) = 0 lies in the interval [0, 1].
(c) Analyze which one of the following three equations you will choose to
approximate the real solution of f(x) = 0 by the fixed-point iteration
method:
(i) x = (1 – x²)³
(1 – x³)
(ii) x =
(iii) x =
(d) Approximate the real solution of f(x) = 0 with an accuracy of 10-4.

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