Question

3. Use the bisection MATLAB program to estimate the roots of the function k(x) = x2 - 4, where x's range is [-1, 3). Include solutions for this method in the report. 4. Write a MATLAB program that uses the false-position method to estimate the roots of the function k(x) in problem#3. Include your m-file and solutions for this method in the report. In addition, submit your m-file separately.

Answer 1

4)

clc%clears screen
clear all%clears history
close all%closes all files
f = @(x) x.^2-4;
e=1e-2;
x0=-1;
x1=3;
i=0;
imax=200;
x2=x1+1;
flag=1;
while (abs(x2-x1)>e)
if(i~=0)
x1=x2;
end
x2=x1-((f(x1)/(f(x1)-f(x0)))*(x1-x0));
x0=x1;
i=i+1;
if(i==200)

disp('the required accuracy is not reached in 100 iterations');
flag=0;
end
end
if(flag==1)
root=x2
else
root=[];
end