7. The equation x² + ax + b = 0, has two real roots a and B. Show that the iteration method

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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7. The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration
method
(i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a | > | B I,
(ii) Xk+1 = - b/(Xk + a), is convergent near x = a, if | a |< | B |.
Transcribed Image Text:7. The equation x² + ax + b = 0, has two real roots a and ß. Show that the iteration method (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a | > | B I, (ii) Xk+1 = - b/(Xk + a), is convergent near x = a, if | a |< | B |.
Solve what is asked. Show your complete solution.
1. Use the method of Successive Approximation to find a real root of e* – x²=0 correct
to four significant
figures.
Transcribed Image Text:Solve what is asked. Show your complete solution. 1. Use the method of Successive Approximation to find a real root of e* – x²=0 correct to four significant figures.
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