Question

The polynomial function f(x) = 3x5 - 2x2 + 7x models the motion of a roller coaster. The roots of the function represent when

Answer 1

Answer:

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