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%.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 32E
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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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