Let \(f(x)=\prod^ n_{i=1}(x-a_ i)\) be a polynomial of degree \(n\) with distinct real zeros which we assume are in increasing order: \(a_ 1<a_ 2<\cdots<a_ n\). Rolle’s theorem tells us that there is exactly one zero of \(f'\) in each interval \((a_ i,a_{i+1})\), and intuitively we feel that the zeros of \(f'\) are more widely or more evenly distributed than those of \(f\). To support this idea, we measure the separation of the zeros by \(\delta(f)=\min_ i(a_{i+1}-a_ i)\) and show that \(\delta(f')>\delta(f)\).