(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].
(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].
ChapterP: Prerequisites
SectionP.4: Factoring Polynomials
Problem 84E: The rate of change of an autocatalytic chemical reaction is kQxkx2 where Q is the amount of the...
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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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Faf7963ce-77e7-4cdb-a67a-db8796a9e0b7%2Fabf6b86b-a8a6-4dff-aa30-51cc4c20b94f%2Fxt39oot_processed.png&w=3840&q=75)
Transcribed Image Text:(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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