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HW2_1 handwork: The equation x³ + 2x² - 10x = 6 has three real roots. Find the largest root that lies in the interval [2.5, 3] using a) bisection method, and b) false position method. For both cases use the es = 0.5% (2 sig fig accuracy). Present your results in tabular forms (shown below, add rows as needed). Also show your calculations for first two iterations below the respective tables. (a) Bisection: xl 2.5 f(xl) (b) False position: f(xl) xl 2.5 xu 3 xu 3 f(xu) f(xu) xm xr ea (%) ea (%) f(xm) f(xr)

HW2_1 handwork: The equation x³ + 2x² - 10x = 6 has three real roots. Find the largest root that lies in the interval [2.5, 3] using a) bisection method, and b) false position method. For both cases use the es = 0.5% (2 sig fig accuracy). Present your results in tabular forms (shown below, add rows as needed). Also show your calculations for first two iterations below the respective tables. (a) Bisection: xl 2.5 f(xl) (b) False position: f(xl) xl 2.5 xu 3 xu 3 f(xu) f(xu) xm xr ea (%) ea (%) f(xm) f(xr)

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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HW2_1 handwork: The equation x³ + 2x² - 10x interval [2.5, 3] using xl 2.5 a) bisection method, and b) false position method. For both cases use the es = 0.5% (2 sig fig accuracy). Present your results in tabular forms (shown below, add rows as needed). Also show your calculations for first two iterations below the respective tables. xl 2.5 (a) Bisection: | f(xl) (b) False position: f(xl) xu 3 - 6 has three real roots. Find the largest root that lies in the xu 3 f(xu) f(xu) xm xr ea (%) ea (%) f(xm) f(xr)
Transcribed Image Text:HW2_1 handwork: The equation x³ + 2x² - 10x interval [2.5, 3] using xl 2.5 a) bisection method, and b) false position method. For both cases use the es = 0.5% (2 sig fig accuracy). Present your results in tabular forms (shown below, add rows as needed). Also show your calculations for first two iterations below the respective tables. xl 2.5 (a) Bisection: | f(xl) (b) False position: f(xl) xu 3 - 6 has three real roots. Find the largest root that lies in the xu 3 f(xu) f(xu) xm xr ea (%) ea (%) f(xm) f(xr)
Expert Solution
Step 1: Description of given data:

We have given equation is x cubed plus 2 x minus 10 x equals 6 has three real roots.

To find the largest root that lies in the interval open square brackets 2.5 comma 3 close square brackets

by using (a) Bisection Method, (b) False position method.

Express the given equation as a function of x as:

x cubed plus 2 x minus 10 x equals 6 rightwards double arrow x cubed plus 2 x minus 10 x minus 6 equals 0

Hence, bold italic f bold left parenthesis bold italic x bold right parenthesis bold space bold equals bold italic x to the power of bold 3 bold plus bold 2 bold italic x bold minus bold 10 bold italic x bold minus bold 6

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