At most, how many unique roots with a fifth degree polynomial function have? a) 5 b) 6 c) 4 d) 10

The main polynomial thereom says that for every polynom f(x) of degree n then the equation f(x)=0 cannot have more than n roots (counting multiplicity).
If you have a fifth degree polynomial function, then the polynom f(x) cannot have more than unique 5 roots (if some of them have multiplicity more than 1, then the number of roots is less).
Hence the correct choice is A.

(1/x + 1)^2 + 6 (1/x + 1) +5