Question

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.

Answer 1

Answer:

$x=\pm 1, \pm 7, \pm \frac{1}{3}, \pm \frac{7}{3}$

Step-by-step explanation:

Given : The polynomial function $f(x)=3x^5-2x^2+7x$ models the motion of a roller coaster. The roots of the function represent when the roller coaster is at ground level.

To find : Write all potential values of when the roller coaster is at ground level?

Solution :

The given function is  $f(x)=3x^5-2x^2+7x$

It is given that the roots of the function represent when the roller coaster is at ground level. i.e. f(x)=0

The factor form of given function is

$3x^5-2x^2+7x=0$

$x(3x^4-2x+7)=0$

By using zero product property, equate each factor equal to 0.

x=0

or $3x^4-2x+7=0$  ...(1)

The equation (1) has no real root.

Applying rational root theorem,

All the possible roots are in the form of

$r=\pm \frac{\text{Factors of constant term}}{\text{Factors of leading term}}$

The leading term is 3 and the constant term is 7.

Factors of 7 are ±1, ±7 and the factors of 3 are ±1 and ±3.

All the possible roots are

$x=\pm 1, \pm 7, \pm \frac{1}{3}, \pm \frac{7}{3}$