Final answer:
The potential rational root of the polynomial function f(x) = 5x + x² - 3 is -2.
Step-by-step explanation:
A potential rational root of a polynomial function can be determined using the Rational Root Theorem. According to the theorem, if a polynomial function has a rational root, it will be of the form ±p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.
In the given polynomial function, f(x) = 5x + x2 - 3, the constant term is -3 and the leading coefficient is 1. Therefore, the potential rational roots can be obtained by finding the factors of -3 and 1.
The factors of -3 are -1, -3, 1, and 3. The factors of 1 are 1 and -1. Therefore, the potential rational roots are -3, -1, 1, and 3.
Based on the options provided, the potential rational root of the polynomial function f(x) = 5x + x2 - 3 is: