format long;
clc;
 
% Function definition
f = @(x) x.^2 - 2;
 
% Initial guesses
a = 1; % f(a) < 0
b = 2; % f(b) > 0
 
% False Position Iteration
for i = 1:10
    r(i) = (a*f(b) - b*f(a)) / (f(b) - f(a)); % False Position formula
 
    % Store absolute error |b - a| at each step
    err(i) = abs(b - a);
 
    % Update a or b
    if f(r(i)) < 0
        a = r(i);
    else
        b = r(i);
    end
end
 
% Display root estimates
disp('Root estimates at each iteration:');
disp(r');
 
% Display absolute error at each step
disp('Absolute error (|b - a|) at each iteration:');
disp(err');
 

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