linear algebra - Given a characteristic polynomial of a matrix A, find the nullity, rank

If i'm only given the characteristic polynomial of a matrix $A$, how would I find the given information:

• Rank


• Nullity



• Number of elements in the eigenvectors of $A$


• Number of elements in the null space of $A$

The only information that i can figure out are:

• the eigenvalues


• the dimensions of the matrix and


• the determinant of the matrix which is the product of the eigenvalues.