Final answer:
The term 'static' is the correct synonym for something that stays the same, signifying unchangeability. Therefore, the correct option is B. static.
Step-by-step explanation:
The question appears to be asking for a synonym for a word that means to stay the same or not change. The word static fits this definition, as it signifies something that is unchanging or fixed in one place. The other options, while similar, have connotations that are not as precisely aligned with the notion of being unchangeable. For example, rooted suggests being firmly planted in place, fixated indicates an intense focus, and grounded means having a solid basis, though it can also reflect immobility.