Linear maps that preserve matrices annihilated at some fixed vector by a polynomial of degree two

In this paper, we characterize linear maps on the space of all $n\times n$ complex matrices which preserve the set of matrices $T$ such that, for some fixed complex numbers $s$ and $p$ and some fixed nonzero vector $x_0\in\mathbb{C }^{n}$, satisfy the equality $$ T^2(x_0)-sT(x_0)+px_0=0. $$