let L be a linear differential operator of the form \(Lu=u^{(n)}+a_ 1(t)u^{(n-1)}+...+a_ n(t)u,\) which is disconjugate on an interval I, where \(a_ i(t)\), \(i=1,2,...,n\) are continuous real functions on an interval \(J\supset I\). Pólya proved that if v is any n times differentiable function on I which has \(n+1\) zeros, then \(Lv(p)=0\) for some point p intermediate to the zeros of v. (We say that an operator is disconjugate on an interval \(I\subset J\) if the only solution of \(Lu=0\) which, counting multiplicities, has n or more zeros in I is the trivial solution.) Clearly the Pólya result is a generalization of Rolle's theorem. The author studies, among other things, the problem of whether the converse of Pólya's theorem, holds. He proves that if L is a real scalar ordinary differential operator which has the Pólya property on a not closed interval I, then L is disconjugate. If I is a closed interval on which Pólya property holds, then L is disconjugate on the interior of I.