bisection method to determine an approximation to the root that is accurate to at least within 10^-4 in matlab

main.m
function root = bisectionMethod(f, a, b, tolerance)
    % Check for valid inputs
    if f(a) * f(b) >= 0
        error('Function must have opposite signs at the interval endpoints.');
    end
    if a >= b
        error('Interval endpoints must be in increasing order.');
    end
    
    % Perform bisection until desired tolerance is reached
    while abs(a - b) >= tolerance
        c = (a + b) / 2;
        
        % Check if root has been found
        if abs(f(c)) < tolerance
            root = c;
            return;
        end
        
        % Update interval bounds
        if f(a) * f(c) < 0
            b = c;
        else
            a = c;
        end
    end
    
    % Calculate the approximation to the root
    root = (a + b) / 2;
end
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main.m
% Define the function f
f = @(x) x^3 - 2*x - 5;

% Define the interval boundaries
a = 1;
b = 3;

% Specify the desired tolerance
tolerance = 10^(-4);

% Call the bisectionMethod function
root = bisectionMethod(f, a, b, tolerance);

% Display the root approximation
disp(['Root: ', num2str(root)]);
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