f = @(x) x^2 - 2;  % Function definition
 
a = 2;
b = 3;
 
for i = 1:8
    r = (a + b) / 2;  % Midpoint calculation
    disp(['Iteration ', num2str(i), ' : r = ', num2str(r)]);
 
    if f(a) * f(r) < 0
        b = r;  % Root lies in [a, r]
    else
        a = r;  % Root lies in [r, b]
    end
 
    err(i) = abs(b - a);
    disp(['Error = ', num2str(err(i))]);
end
 
fprintf('\nFinal root estimate after 8 iterations: %.10f\n', r);
# your code goes here

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