Question

The following cubic polynomial has three real roots p(x) = 32x³ − 110x² + 123x − 45

(a) Plot p(x) for .9 ≤ x ≤ 1.6 and indicate the locations of the three roots. What are the exact roots of p(x)?

(b) Write a MATLAB code to run Newton’s method with x₀ = 1.2 and discuss the convergence.

(c) Write a MATLAB code to run the secant method starting with x₀ = 1.31 and x₁ = 1.2 and discuss the convergence.

(d) Write a MATLAB code to run the bisection method with the initial bracket [.9, 1.6] and discuss the convergence.

Answer 1

`Hey,

Note: If you have any queries related the answer please do comment. I would be very happy to resolve all your queries.

a)

clc%clears screen
clear all%clears history
close all%closes all files
format long;
C=[32,-110,123,-45];
f=@(x) polyval(C,x);
hold on;
fplot(f,[0,2]);
disp('Exact roots');
R=roots(C)
plot(R,f(R),'*');

b)

clc%clears screen
clear all%clears history
close all%closes all files
format long;
C=[32,-110,123,-45];
f=@(x) polyval(C,x);
g=@(x) polyval(polyder(C),x);
x0=1.2;
for i=1:100
x0=x0-f(x0)/g(x0);
end
disp('Root is');
disp(x0);

Note: Brother According to Chegg's policy we are only allowed to answer first 2 part if there are many. So, I request you to post other part as separate posts

Kindly revert for any queries

Thanks.