Two theorems are proved about the zeros of certain Jacobi polynomials that are important in the theory of interpolation and approximation.THEOREM 1. Let$S_k $and$\bar S_k $be the sums of thekth powers of the zeros of$P_n^{(w, - w)} (x)$and$P_n^{(w, - w)} ( - x)$respectively (wreal, $0 < w < 1$). Then for$k = 1,2, \cdots ,2n,S_k - \bar S_k = - 2w$ (kodd) or$= 0$ (keven).THEOREM 2. Let$S_k $and$\bar S_k $be the sums of thekth powers of$P_{n + 1}^{( - w,w - 1)} (x)$and$P_n^{(w,1 - w)} (x)$respectively (wreal, $0 < w < 1$).Then for$k = 1,2, \cdots ,2n + 1,S_k - \bar S_k = 2w - 1$ (kodd) or$ = 1$(keven).