Finding Roots Using Binary or Interpolation Search

In general the secant method (interpolation search) converges faster than the binary search. However there are exceptions to this rule, as shown in the cubic example; the binary search converges neatly, whereas the multiple root causes a derivative to be zero, sending the interpolation far away. Such conditions can be very unfortunate for the secant method, but they can be avoided: multiple roots can be eliminated using algebraic methods, like dividing the polynomial by its derivative.