Bairstow's MethodStopping Criteria: 0.00005Please show algebra. Thank you!Refer to the example. Solve for all the roots of x using Bairstow's Method starting at rị = 0.25 and s1 = 8.75 of the polynomialf(x)=x*+8x +72x – 81 ExampleFind the roots off(x) = x' – 3x? + 4x – 2 = 0-From the given equation,az = 1.0a, = -3.0a, = 4.0a, = -2.0We initially guess values for r and s. For thisproblem, we'll have r, = 1.5 and s, = -2.5Tabular Solution1-34-2, = 1.51.5-2.25-1.125S1 = -2.5-2.53.751-1.5-0.750.625= 1.51.5S, = -2.5-2.51-3.25+ (-)(0'0)Ar4 (1.0)As = 0.75(-)-3.25Ar + (0.0)As =-0.625SolutionSolving simultaneouslyAr = 0.192308andAs = 0.75Andr2 = r; + Ar = 1.5+0.192308 =1.692308S2 = S, + As = -2.5+0.75 = -1.75Then we use the new set of values of r and suntil such time that...Tabular SolutioniArAs1-34-2r. =1.99999911.5-2.50.1923080.751.999999-2.000001S6 = -2-221.692308-1.750.278352-0.1440411-1.00000131.97066-1.8940410.034644-0.1100911.9999991.999999242.005304-2.004132-0.0053170.004173$6 = -2-21.999987-1.9999590.000012-0.00004110.99999861.999999-2

Name: Bairstow's MethodStopping Criteria: 0.00005Please show algebra. Thank
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Description: Bairstow's MethodStopping Criteria: 0.00005Please show algebra. Thank you!Refer to the example. Solve for all the roots of x using Bairstow's Method starting at rị = 0.25 and s1 = 8.75 of the polynomialf(x)=x*+8x +72x – 81 ExampleFind the roots off(x

The polynomial for which the roots has to be found is given as follows: fx=x4+8x3+72x-81 We are…

Answered: Solve for all the roots of x using…

Math

Advanced Math

Solve for all the roots of x using Bairstow's Method starting at ri = 0.25 and s1 = 8.75 of the polynomial f(x)=x*+8x +72x – 81

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 14T

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Bairstow's Method

Stopping Criteria: 0.00005

Please show algebra. Thank you!

Refer to the example.

Solve for all the roots of x using Bairstow's Method starting at rị = 0.25 and s1 = 8.75 of the polynomial
f(x)=x*+8x +72x – 81

Example
Find the roots of
f(x) = x' – 3x? + 4x – 2 = 0
-
From the given equation,
az = 1.0
a, = -3.0
a, = 4.0
a, = -2.0
We initially guess values for r and s. For this
problem, we'll have r, = 1.5 and s, = -2.5
Tabular Solution
1
-3
4
-2
, = 1.5
1.5
-2.25
-1.125
S1 = -2.5
-2.5
3.75
1
-1.5
-0.75
0.625
= 1.5
1.5
S, = -2.5
-2.5
1
-3.25
+ (-)
(0'0)Ar4 (1.0)As = 0.75
(-)
-3.25Ar + (0.0)As =-0.625
Solution
Solving simultaneously
Ar = 0.192308
and
As = 0.75
And
r2 = r; + Ar = 1.5+0.192308 =1.692308
S2 = S, + As = -2.5+0.75 = -1.75
Then we use the new set of values of r and s
until such time that...
Tabular Solution
i
Ar
As
1
-3
4
-2
r. =
1.999999
1
1.5
-2.5
0.192308
0.75
1.999999
-2.000001
S6 = -2
-2
2
1.692308
-1.75
0.278352
-0.144041
1
-1.000001
3
1.97066
-1.894041
0.034644
-0.110091
1.999999
1.999999
2
4
2.005304
-2.004132
-0.005317
0.004173
$6 = -2
-2
1.999987
-1.999959
0.000012
-0.000041
1
0.999998
6
1.999999
-2

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