The bisection method

If f(x) is real and continuous in the range from xi to xf f(xf) have opposite signs, then there is at least one real root between intervals.
The bisection method is a type of incremental search in which the interval is always divided in half. If the value of the function changes sign on an interval, we evaluate the value of the function at the midpoint.

Root position is determined at the point half the subinterval in which a sign change occurs.
This process is repeated to achieve the best approximation.