The polynomial function f(x) = 3x5 - 2x2 + 7x models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level. Which answer choice represents all potential values of when the roller coaster is at ground
level? Begin by factoring x to create a constant term.
O 0, +7.+1, , 13
0 0,43. 41. t. 27

0, ±1, ±7,±1/3, and ±7/3

Step-by-step explanation:

In the function:

3x^5 - 2x² + 7x

x can be extracted as the greatest common factor, as follows:

x(3x^4 - 2x + 7)

then, zero is one root of the function.

According to Rational Root Theorem:

possible rational roots = factors of the constant/factors of the leading coefficient

For this case, factors of the constant (7) are: ±1 and ±7

For this case, factors of the leading coefficient (3) are: ±1 and ±3

Then:

possible rational roots =  ±1/±1, ±7/±1, ±1/±3 and ±7/±3. Simplifying: ±1, ±7,±1/3, and ±7/3