Final answer:
The polynomial function has a number of zeros that can be determined using the Rational Root Theorem and the Fundamental Theorem of Algebra.
Step-by-step explanation:
The given polynomial function is: f(x) = x^5 - 2x^4 + 14x^3 - 28x^2 + 49x - 98
To find the number of zeros the polynomial function will have, we need to count the number of times the function crosses the x-axis. Each crossing represents a zero. We can use the Rational Root Theorem and the Fundamental Theorem of Algebra to determine the number of zeros. However, determining the actual values of the zeros requires additional calculations or the use of a graphing calculator.
Using the Rational Root Theorem, we can find the potential rational zeros by considering the factors of the constant term (-98) divided by the factors of the leading coefficient.
In this case, the potential rational zeros include ±1, ±2, ±7, ±14, ±49, and ±98. By testing these values, we can determine if any of them are the actual zeros of the function.