  In this paper, we propose a unified approach for solving structure-preserving
eigenvalue embedding problem (SEEP) for quadratic regular matrix polynomials
with symmetry structures. First, we determine perturbations of a quadratic
matrix polynomial, unstructured or structured, such that the perturbed
polynomials reproduce a desired invariant pair while maintaining the invariance
of another invariant pair of the unperturbed polynomial. If the latter is
unknown, it is referred to as no spillover perturbation. Then we use these
results for solving the SEEP for structured quadratic matrix polynomials that
include: symmetric, Hermitian, $\star$-even and $\star$-odd quadratic matrix
polynomials. Finally, we show that the obtained analytical expressions of
perturbations can realize existing results for structured polynomials that
arise in real-world applications, as special cases. The obtained results are
supported with numerical examples.
