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Determine the real root of f(x) = 5x³5x² + 6x-2 using bisection to locate the root. Employ initial guesses of x₁ = 0 and Xu = 1 and iterate until the estimated error & falls below a level of & = 10%.

Determine the real root of f(x) = 5x³5x² + 6x-2 using bisection to locate the root. Employ initial guesses of x₁ = 0 and Xu = 1 and iterate until the estimated error & falls below a level of & = 10%.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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PLS ANSWER NO. 1
Solve the following problems. Tabulate all answers. Show the complete solution of one iteration only. Write all values accurate to 5-decimal places ONLY. 1. Determine the real root of f(x) = 5x³ - 5x² + 6x - 2 using bisection to locate the root. Employ initial guesses of x₁ = 0 and xu = 1 and iterate until the estimated error & falls below a level of Es = 10%. 2. Find all real roots of f(x) = x4 -8x³ - 35x² + 450x-1001 using the false-position method. Use initial guesses of x₁ = 4.5 and x = 6 and perform five iterations. Compute both the true and approximate errors based on the fact that the root is 5.60979. Perform the computation to within &, = 1.0 %.
Transcribed Image Text:Solve the following problems. Tabulate all answers. Show the complete solution of one iteration only. Write all values accurate to 5-decimal places ONLY. 1. Determine the real root of f(x) = 5x³ - 5x² + 6x - 2 using bisection to locate the root. Employ initial guesses of x₁ = 0 and xu = 1 and iterate until the estimated error & falls below a level of Es = 10%. 2. Find all real roots of f(x) = x4 -8x³ - 35x² + 450x-1001 using the false-position method. Use initial guesses of x₁ = 4.5 and x = 6 and perform five iterations. Compute both the true and approximate errors based on the fact that the root is 5.60979. Perform the computation to within &, = 1.0 %.
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