Final answer:
All three given roots (2, 3, and 9/2) of the function f(x) are rational numbers, thus the answer to the question is three.
Step-by-step explanation:
The question asks, How many roots of f(x) are rational numbers, given the roots 2, 3, and 9/2. A rational number is defined as a number that can be expressed as the quotient or fraction p/q of two integers, where the denominator q is not zero. All of the provided roots, 2, 3, and 9/2, meet these criteria, as they can be written as fractions with an integer numerator and a non-zero integer denominator.
Therefore, the answer to how many roots of f(x) are rational numbers is three, since all listed roots (2, 3, and 9/2) are rational.
The number of rational roots of a function can be determined by analyzing its equation. In this case, we need to determine how many roots of the equation f(x) = 0 are rational numbers. By examining the roots given (2, 3, 9/2), we can see that all three roots are rational numbers. Therefore, the function f(x) has 3 rational roots.