Equivalence partitioning for method that calculates the number of roots of a polynomial

I need help with assignment in Program Verification, where i have to find at least 5 equivalence classes for the method that gives the number of roots of a non-zero polynomial determined by the coefficients given as a parameter.

All i have is method signature "unsigned roots (float a0, ...)" It takes at least one parameter.

All i can derive from specifications and method signature are 2 classes: 1. Valid - (at least parameter must be unequal zero) 2. Invalid - (the opposite, all parameters are equal zero)

How could i come up with 3 more equivalence classes?

Thanks