function result = functionDemo(x)
    result = x^3 - 23*x^2 + 142*x - 120;
end











function [root, iterations, errors] = bisection_method(guess1, guess2, max_iterations, tolerance)
    if functionDemo(guess1) * functionDemo(guess2) >= 0
        error("The guesses do not satisfy the required conditions");
    end

    iterations = 0;
    errors = [];
    prevGuess = 0;

    while iterations < max_iterations
        root = (guess1 + guess2) / 2;
        error_estimate = abs(root - prevGuess);
        errors = [errors; error_estimate];

        if error_estimate < tolerance
            break;
        end

        prevGuess = root;

        if functionDemo(guess1) * functionDemo(root) < 0
            guess2 = root;
        else
            guess1 = root;
        end

        iterations = iterations + 1;
    end
endfunction










[root, iterations, errors] = bisection_method(11, 20, 100, 1e-6);










% Plotting the graph of relative errors vs. iterations
figure;
plot(1:length(errors), errors, '-o');
xlabel('Iterations');
ylabel('Relative Error');
title('Relative Errors vs. Iterations');
grid on;