The authors develop asymptotic approximations for the zeros of the functions Gi and Hi, where
and it is a particular solution of the differential equation and
and it is a solution of . As it is known , is the non-homogeneous Airy differential equation and the functions Gi and Hi are called the Scorer functions. The authors study qualitative properties of the real zeros of Gi and as well as asymptotics of the negative zeros of Gi. They also study the complex zeros of Gi, and Hi. Tables are given with numerical values of the zeros.