Let D be a (2 s + 1)-design with parameters ( v, k, λ 2 s + 1 ). It is known that D has at least s + 1 block intersection numbers x 1, x 2, …, x s + 1 . Suppose now D is an extremal (2 s + 1)-design with exactly s + 1 intersection numbers. In this case we give a short proof of the following known result of Delsarte: The s + 1 intersection numbers are roots of a polynomial whose coefficients depend only on the design parameters. Delsarte's result, proved more generally, for designs in Q-polynomial association schemes, uses the notion of the annihilator polynomial. Our proof relies on elementary ideas and part of an algorithm used for decoding BCH codes.