Final answer:
The rational roots of the polynomial 2x^4 - 5x^3 - 2x^2 - 3x + 8 can be found using the Rational Root Theorem, leading to possible rational roots of ±(1, 1/2, 2, 4, 8), corresponding to option a) ±(1, ±2, ±4, ±8).
Step-by-step explanation:
The rational roots of a polynomial can be predicted using the Rational Root Theorem, which states the possible rational roots are 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 polynomial f(x) = 2x^4 - 5x^3 - 2x^2 - 3x + 8, the constant term is 8 and the leading coefficient is 2. Therefore, the possible values for p are ±(1, 2, 4, 8) and the possible values for q are ±(1, 2).
When we list out the possible p/q combinations, we eliminate duplicates and get the set of possible rational roots: ±(1, 1/2, 2, 4, 4/2, 8, 8/2). Simplifying the fractions, we end up with ±(1, 1/2, 2, 4, 8), which corresponds to option a) ±(1, ±2, ±4, ±8).