I'm stuck on this problem :
Suppose that we use the bisection method to find some roots of a continuous function f(x) in the interval [a,b] and that f(a)f(b)<0.
Suppose also that x_i, i goes from 1 to k are the roots of f(x) in [a,b], they are simple roots (what I understand by this is that they are not double roots) and that x_1<x_2<...<x_k.
1)Study the parity of k.
I will try to do the other questions of this problem once I understand how to do the 1).
Ohh... I think I just understood. By doing a draw, I notice that if the number of roots is odd then f(a)f(b)<0 and if it's even, f(a)f(b)>0. How can I prove that?