Answer:
(b) 0, ±1/3, ±1, ±7/3, ±7
Explanation:
You want the potential rational roots of the polynomial 3x^5 -2x^2 +7x.
Rational root theorem
The rational root theorem tells you potential rational roots will have a numerator that is a divisor of the polynomial's constant term, and a denominator that is a divisor of the leading coefficient.
The given polynomial can be factored as ...
x(3x^4 -2x +7)
so any rational roots will be in the set ...
{0, ±(divisor of 7)/(divisor of 3)} = {0, ±1/3, ±1, ±7/3, ±7}
__
Additional comment
A graph of the polynomial shows it to be monotonic, with a real zero only at x=0. This roller coaster, while steep, wouldn't have any valleys.
The question asks only for x-intercepts. The answer choices are what suggest that rational x-intercepts are the ones of interest.