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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.