## Stuck on an Analysis problem

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.
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?