  In this paper, we present some necessary and sufficient conditions under
which an irreducible polynomial is self-reciprocal (SR) or
self-conjugate-reciprocal (SCR). By these characterizations, we obtain some
enumeration formulas of SR and SCR irreducible factors of $x^n-\lambda$,
$\lambda\in \Bbb F_q^*$, over $\Bbb F_q$, which are just open questions posed
by Boripan {\em et al} (2019). We also count the numbers of Euclidean and
Hermitian LCD constacyclic codes and show some well-known results on Euclidean
and Hermitian self-dual constacyclic codes in a simple and direct way.
