Bracket a model crossing before applying bisection

Define the task

A root marks a point where a function equals zero. When searching for a model prediction equal to a target, subtract the target from the prediction first. Define the allowed input interval and units. A crossing outside that interval may have no scientific meaning even if the equation admits it.

Carry out the check

Bisection requires a continuous function and opposite signs at the bracket endpoints, unless an endpoint is already a root. Evaluate the midpoint and retain the half that brackets the sign change. Stop when the bracket width meets the stated tolerance, and report both the approximate root and the remaining interval. An iteration limit is a stopping safeguard and does not itself establish convergence.

Worked hypothetical example

For the hypothetical equation x²−2=0, endpoints 1 and 2 give values −1 and 2. The midpoint 1.5 gives 0.25, leaving the bracket from 1 to 1.5. Further subdivisions converge toward about 1.414214. The other root lies outside this bracket. Even-multiplicity roots can touch zero without changing sign, so failure to find a bracket does not prove that no root exists.

Method checked 14 November 2026 against SciPy documentation: bisect.

Open the polynomial bisection calculator.

Download the root bracket decision record.