Final answer:
The polynomial function g(s) = 4s⁵ - s³ + 2s⁷ - 2 can have up to 7 roots or zeros, as dictated by the highest degree of the polynomial which is 7.
Step-by-step explanation:
The equation g(s) = 4s⁵ - s³ + 2s⁷ - 2 is a polynomial equation. To identify how many zeros the function has, we are searching for the roots of the polynomial, which are the values of s that make g(s) equal to zero. However, g(s) is already in its expanded form, and without further algebraic manipulation or graphing tools, we cannot directly find the roots. As a function of s, with s being a real or complex number, the Fundamental Theorem of Algebra tells us that a polynomial of degree n will have exactly n roots, counting multiplicity and including complex roots. Hence, since the highest degree of s in g(s) is 7, there can be upto 7 zeros for g(s).