% given a & b such that f(a)f(b)<0, find c in (a,b) such that f(c) = 0
a = 1;
b = 2;
ep = 10^-4;             % the error tolerance
max_iterate = 10000;    % the maximum of the iteration steps

if a >= b
    disp('a < b is not true.  Stop!')
    return
end

fa = f(a); fb = f(b);
if sign(fa)*sign(fb) > 0
    disp('f(a0) and f(b0) are of the same sign.  Stop!')
    return
end

c = (a+b)/2; 
it_count=0; %it_count is the iteration steps, starting with 0

while ( b-c > ep & it_count < max_iterate )
    it_count = it_count + 1;
    fc = f(c);
    if sign(fb)*sign(fc) <= 0
        a = c;
        fa = fc;
    else
        b = c;
        fb = fc;
    end
    c = (a+b)/2;
end

it_count
format long e
root = c
error_bound = b-c

function value = f(x)
    value = x^2 - 3;
end