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5.5 (a) Determine the roots of f(x)=-12 – 21x + 18x2 – 2.75x³ graphically. In addition, determine the first root of the function with (b) bisection and (c) false position. For (b) and (c) use initial guesses of xị = -1 and xy = 0 and a stopping criterion of 1%.

5.5 (a) Determine the roots of f(x)=-12 – 21x + 18x2 – 2.75x³ graphically. In addition, determine the first root of the function with (b) bisection and (c) false position. For (b) and (c) use initial guesses of xị = -1 and xy = 0 and a stopping criterion of 1%.

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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5.5 (a) Determine the roots of f(x)= -12 – 21x + 18x2 – 2.75x graphically. In addition, determine the first root of the function with (b) bisection and (c) false position. For (b) and (c) use initial guesses of xị = -1 and xy = 0 and a stopping criterion of 1%.
Transcribed Image Text:5.5 (a) Determine the roots of f(x)= -12 – 21x + 18x2 – 2.75x graphically. In addition, determine the first root of the function with (b) bisection and (c) false position. For (b) and (c) use initial guesses of xị = -1 and xy = 0 and a stopping criterion of 1%.
a + b C = 2 a f(a) b f(b) f(c) Update 1 -1 29.75 -12 -0.5 3.3438 a = c 2 -0.5 3.3438 -12 -0.25 -5.582 b = c 3 -0.5 3.3438 -0.25 -5.582 -0.375 -1.4487 b = c 4 -0.5 3.3438 -0.375 -1.4487 -0.4375 0.8631 a = c 5 -0.4375 0.8631 -0.375 -1.4487 -0.4062 -0.3137 b = c -0.4375 0.8631 -0.4062 -0.3137 -0.4219 0.2695 a = c 7 -0.4219 0.2695 -0.4062 -0.3137 -0.4141 -0.0234 b = c 8 -0.4219 0.2695 -0.4141 -0.0234 -0.418 0.1227 a = c -0.418 0.1227 -0.4141 -0.0234 -0.416 0.0496 a = c 10 -0.416 0.0496 -0.4141 -0.0234 -0.415 0.0131 a = c 11 -0.415 0.0131 -0.4141 -0.0234 -0.4146 -0.0052 b = c 6. 9,
Transcribed Image Text:a + b C = 2 a f(a) b f(b) f(c) Update 1 -1 29.75 -12 -0.5 3.3438 a = c 2 -0.5 3.3438 -12 -0.25 -5.582 b = c 3 -0.5 3.3438 -0.25 -5.582 -0.375 -1.4487 b = c 4 -0.5 3.3438 -0.375 -1.4487 -0.4375 0.8631 a = c 5 -0.4375 0.8631 -0.375 -1.4487 -0.4062 -0.3137 b = c -0.4375 0.8631 -0.4062 -0.3137 -0.4219 0.2695 a = c 7 -0.4219 0.2695 -0.4062 -0.3137 -0.4141 -0.0234 b = c 8 -0.4219 0.2695 -0.4141 -0.0234 -0.418 0.1227 a = c -0.418 0.1227 -0.4141 -0.0234 -0.416 0.0496 a = c 10 -0.416 0.0496 -0.4141 -0.0234 -0.415 0.0131 a = c 11 -0.415 0.0131 -0.4141 -0.0234 -0.4146 -0.0052 b = c 6. 9,
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