The article shows that in a system of three particles with certain types of interactions, if there are no negative-energy bound states or zero-energy resonances in pairs of particles, then the eigenvalues are absorbed at zero energy. If even one pair of particles has a zero-energy resonance, a zero-energy ground state for all three particles cannot exist. The researchers also demonstrate that by adjusting the coupling constants of the interactions, it is possible to have the lowest energy level at zero and find a negative-energy ground state with specific properties.