2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56644Quadratic algebras of the type $\lsb Q_0, Q_\pm \rsb$ $=$ $\pm Q_\pm$, $\lsb Q_+, Q_- \rsb$ $=$ $aQ_0^2 + bQ_0 + c$ are studied using three-mode bosonic realizations. Matrix representations and single variable differential operator realizations are obtained. Examples of physical relevance of such algebras are given.17 pages, Latex, Submitted to Journal of Mathematical PhysicsMathematical PhysicsExactly Solvable and Integrable SystemsQuantum Physicstext