Final answer:
A polynomial of degree 7, such as the given polynomial function f(x), will have 7 solutions which can be real or complex numbers including repeated solutions.
Step-by-step explanation:
The function f(x) = 5x^7 – 3x^4 – 2x^2 +9 is a polynomial of degree 7. According to the Fundamental Theorem of Algebra, a polynomial of degree n will have exactly n solutions in the complex number system. This means that our seventh-degree polynomial will have 7 solutions. It's important to note that these solutions could be real or complex and some may be repeated.