TheAlgorithms/Python · error · ValueError

could not find root in given interval.

Error message

could not find root in given interval.

What it means

Error "could not find root in given interval." thrown in TheAlgorithms/Python.

Source

Thrown at maths/numerical_analysis/bisection.py:32

    1.0
    >>> bisection(lambda x: x ** 2 - 4 * x + 3, 2, 4)
    3.0
    >>> bisection(lambda x: x ** 2 - 4 * x + 3, 4, 1000)
    Traceback (most recent call last):
        ...
    ValueError: could not find root in given interval.
    """
    start: float = a
    end: float = b
    if function(a) == 0:  # one of the a or b is a root for the function
        return a
    elif function(b) == 0:
        return b
    elif (
        function(a) * function(b) > 0
    ):  # if none of these are root and they are both positive or negative,
        # then this algorithm can't find the root
        raise ValueError("could not find root in given interval.")
    else:
        mid: float = start + (end - start) / 2.0
        while abs(start - mid) > 10**-7:  # until precisely equals to 10^-7
            if function(mid) == 0:
                return mid
            elif function(mid) * function(start) < 0:
                end = mid
            else:
                start = mid
            mid = start + (end - start) / 2.0
        return mid


def f(x: float) -> float:
    return x**3 - 2 * x - 5


if __name__ == "__main__":

View on GitHub (pinned to f5988cc097)

Solutions

1. Choose an interval [a, b] where f(a) and f(b) have opposite signs.
2. Widen the search interval or plot the function to locate a sign change.

When it happens

Trigger: Thrown at maths/numerical_analysis/bisection.py:32 when the library encounters an invalid state.

Common situations: See trigger scenarios.

AI-assisted analysis of TheAlgorithms/Python@f5988cc097 (2026-08-14). Data as JSON: /api/errors/e931f1b4cec27257. Report an issue: GitHub.