I'm stuck on this problem :

Suppose that we use the bisection method to find some roots of a continuous function in the interval and that .

Suppose also that , goes from to are the roots of in , they are simple roots (what I understand by this is that they are not double roots) and that .

1)Study the parity of .

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 and if it's even, . How can I prove that?