Design an algorithm,have polynomial complexity for deciding satisfiability of a 1-conjective Normal Form boolean formula
Most satisfiability algorithms do actually find an assignment for the variables to satisfy the equation, but in your case (a conjunction of single variables) this is not necessary.

When the entire logic formula is just a single conjunction of variables, the only way it is not satisfiable is if it contains both $a$ and $\neg a$. If there is no variable which is contained both positive and negatively in the formula, the formula is satisfiable.