<p>The exact solution for the Einstein–Maxwell field equations is generated. The quadratic equation of state together with the Karmarkar condition are used to investigate the structure and properties of the relativistic stars. The Karmarkar condition provides the relationship between the two gravitational potentials. The process of combining the Karmarkar condition and an EoS has currently led to new realistic solutions. In generating the model, one of the gravitational potentials is specified on physical grounds. The generated model undergoes several physical tests to determine its validity and acceptability. Several realistic physical conditions are found to be satisfied. The model stability regarding the adiabatic index and equilibrium of the physical forces is satisfied. The mass–radius relationship and surface red-shift both increase monotonically and are within the acceptable range of a realistic model. Their parameter values are found to be compatible with observations. The gravitational potentials are continuous throughout the star’s interior, and the model’s energy conditions are also satisfied.</p>