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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 |>|ß |. (ii) Xk+1 =– b/(xk+ a), is convergent near x = a, if | a |<|ß |.

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 |>|ß |. (ii) Xk+1 =– b/(xk+ a), is convergent near x = a, if | a |<|ß |.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.5: Rational Functions
Problem 7E
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M3.7 solve and show the complete solution.

7. The equation x? + ax + b = 0, has two real roots a and B. Show that the iteration method (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a |>|ß ], (ii) Xk+1 =- b/(Xk+ a), is convergent near x = a, if | a |<| B |.
Transcribed Image Text:7. The equation x? + ax + b = 0, has two real roots a and B. Show that the iteration method (i) Xk+1 = - (axk + b)/xk, is convergent near x = a, if | a |>|ß ], (ii) Xk+1 =- b/(Xk+ a), is convergent near x = a, if | a |<| B |.
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