Question

6.4 Consider the following function:3x^4 - 6x =6a. Put the function in standard form, and plot the function using MATLAB.b. Write a simple program using the Bisection Method to find any oneroot of the equation to within 0.01.c. Write a simple MATLAB script to find the solution to the polynomialequation using the roots command.d. Check your results using the Excel Goal Seek tool.

Answer 1

Program Screenshot:

Sample Output:

Code to copy:

clear all; close all; clc
% a.Solution
num = -5:0.01:5;
fn = @(x) 3*(x.^4)-6.*x-6;
figure; plot(num,fn(num));
title('Part (a) Plot of y = 3x^4-6x-6');
xlabel('x'); ylabel('y');

% b.Solution
% Bisection method
disp('f(a)<0 and f(b)>0 or f(a)>0 and f(b)<0');
a = input('Enter the value of a :');
b = input('Enter the value of b :');
TL = 0.01;
MAX = 500;
N = 1;
while(N <= MAX)
re = (a+b)/2;
if (fn(re) == 0 || (b-a)/2 < TL)
fprintf('%.4f is a root of the equation \n',re);
break;
end
N = N+1;
if (fn(re)*fn(a) > 0)
a = re;
else
b = re;
end
end

% c.Solution
%represents the polynomial coefficients as a row vector
pc=[3 0 0 -6 -6];
r=roots(pc);
disp('The roots of the equation are: ');
disp(r);

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d.

Check the result using Excel Goal Seek Tool

Procedure:

1. Open Excel worksheet.

2. Enter x in cell B3 and y in cell C3.

3. In the cell C4, enter the formula (=3*POWER(C4,4)-6*B4-6) as shown in the below excel sheet.

1. Click on the Data menu and then click What-If Analysis, and then select Goal Seek option.
2. In the Set cell box (C4), enter the reference for the cell that contains the formula.
3. In the To value box, type the formula result that you want. In our case, this is 0.
4. In the By changing cell box, enter the reference for the cell that contains the value that you want to adjust. In our case, this reference is cell B4.
5. Goal Seek operation leads to the root whose value is closest to the value in cell B4.

Hence, enter the value in cell B4 appropriately to obtain the roots.