Question

a. Estimate the roots of the equation

 

by plotting the equation.

b. Use the estimates found in part a to nd the roots more accurately with the fzero function.

Answer 1

Program plan:

a. To write a matlab code to find the roots of the equation by plotting the equation.

b. To find the roots with the help of ‘fzero’ function.

 

Program:

%**********************************************************

%A matlab code is written to find the roots of the given

%equation by plotting the equation. The roots are more

%accurately found with the help of ‘fzero’ function.

%**********************************************************

%Declaration of the array

x=-5:0.01:5;

%Anonymous function

f=@(x) x.^3-3.*x.^2+5.*x.*sin(pi.*x/4-5.*pi/4)+3;

%Function plot

plot(x,f(x));

%Command for creating array

grid on;

%Command for setting appropriate axes

axis([-2,5,-50,50])

%Displays text

disp(\'The roots are\');

%Finds the root near \'2\'

x1=fzero(f,2);

%Finds the root near \'0\'

x2=fzero(f,0);

%Finds the root near \'4\'

x3=fzero(f,4);

%Displays value

disp(x1);

%Displays value

disp(x2);

%Displays value

disp(x3);

 

Output (a):

 

Output (b):

>> untitled

The roots are

1.1346

-0.4795

3.8318

Output

>> untitled

The roots are

1.1346

-0.4795

3.8318