Summary: The nature of spurious roots discovered by \textit{G. W. F. Drake} and \textit{S. P. Goldman} [Phys. Rev. A 23, 2093 (1981)] among solutions of the algebraic Dirac Hamiltonian eigenvalue problem is discussed. It is shown that the spurious roots represent the positive spectrum states of the Dirac Hamiltonian and that each of them has its variational non-relativistic counterpart. Sufficient conditions to avoid the appearance of spurious roots in the forbidden gap of Dirac energies are formulated. Numerical examples for \(\kappa= 1(P_{1/2})\) states of an electron in a spherical Coulomb potential (in Slater-type bases) are presented.