write a matlab code based on bisection and false position methods to find the root of an equation. determine the root of 𝑓(𝑥) = (0.9−0.4𝑥)/𝑥 in matlab

main.m
function root = findRoot()
    % Define the function
    f = @(x) (0.9 - 0.4 * x) ./ x;

    % Define the interval [a, b] within which the root lies
    a = -1;
    b = 1;

    % Define the desired accuracy
    epsilon = 1e-6;

    % Perform bisection method
    x_bisec = bisectionMethod(f, a, b, epsilon);
    fprintf('Root found using Bisection method: %f\n', x_bisec);

    % Perform false position method
    x_falsepos = falsePositionMethod(f, a, b, epsilon);
    fprintf('Root found using False Position method: %f\n', x_falsepos);

    % Output the root found
    root = x_falsepos;
end

function root = bisectionMethod(f, a, b, epsilon)
    % Check if the interval contains a root
    if f(a) * f(b) >= 0
        error('The interval does not contain a root or contains multiple roots.')
    end

    % Perform the bisection method
    while abs(b - a) > epsilon
        c = (a + b) / 2;
        if f(c) == 0
            break;
        elseif f(a) * f(c) < 0
            b = c;
        else
            a = c;
        end
    end

    % Return the root
    root = (a + b) / 2;
end

function root = falsePositionMethod(f, a, b, epsilon)
    % Check if the interval contains a root
    if f(a) * f(b) >= 0
        error('The interval does not contain a root or contains multiple roots.')
    end

    % Perform the false position method
    while abs(b - a) > epsilon
        c = (a * f(b) - b * f(a)) / (f(b) - f(a));
        if f(c) == 0
            break;
        elseif f(a) * f(c) < 0
            b = c;
        else
            a = c;
        end
    end

    % Return the root
    root = (a * f(b) - b * f(a)) / (f(b) - f(a));
end

% Call the main function
findRoot();
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