Intermediate value theorem/x^3-4x+2/Bisection method/Example

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We want to determine approximately a zero for the polynomial

with the help of the method given by the intermediate value theorem. We have and , hence by fact there must be a zero inside the interval . We compute the value of the function at the arithmetic mean of the interval, which is , and get

Hence we have to continue with the right half of the interval . The arithmetic mean thereof is . The value of the function at this point is

So now we have to continue with the left part of the interval, namely . Its arithmetic mean is . The value of the function at this point is

Therefore we know that there is a zero between and .