write a matlab program that uses the bisection method to determine an approximation to the root that is accurate to at least within 10−4 for in matlab

main.m
function root = bisection_method(f, a, b, tol)
    % f: the function whose root we wish to find
    % a, b: the initial interval [a, b] where the root lies
    % tol: the desired tolerance for the accuracy of the root approximation
    
    % check if the function has different signs at a and b
    if sign(f(a)) == sign(f(b))
        error('Function has the same sign at points a and b. Cannot use bisection method.')
    end
    
    % initialize the root approximation
    root = (a + b) / 2;
    
    % iterate until the desired tolerance is achieved
    while abs(f(root)) > tol
        % check which half the root lies in and update the interval
        if sign(f(a)) == sign(f(root))
            a = root;
        else
            b = root;
        end
        
        % update the root approximation
        root = (a + b) / 2;
    end
end

% Example usage:
f = @(x) x^3 - 2*x - 5;  % define the function
a = 2;  % initial lower bound of the interval
b = 3;  % initial upper bound of the interval
tol = 1e-4;  % desired tolerance

root = bisection_method(f, a, b, tol);  % find the root approximation
disp(root);  % print the root approximation
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