SOLUTION: 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. What values pot

Algebra ->  Rational-functions -> SOLUTION: 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. What values pot      Log On


   

Question 934558: 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. What values potentially represent when the roller coaster is at ground level?
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Find the roots. Factor as much as possible. Show the exponents as intended in your given polynomial:

f(x) = 3x^5 – 2x^2 + 7x
which looks like this when render tags included
f%28x%29+=+3x%5E5+%96+2x%5E2+%2B+7x

Obviously one of the roots will be x=0.
You find the other roots using synthetic division to test the possible roots of -1, -7, -1/3, -7/3, and their opposites.

Be aware, the dividend to start with for synthetic division must include terms with coefficients of 0:
3x%5E5%2B0%2Ax%5E4%2B0%2Ax%5E3%962x%5E2%2B7x
----the site's rendering is failing there and I do not know why-------
highlight_green%283x%5E4%2B0%2Ax%5E3%2B0%2Ax%5E2-2x%2B7%29, THIS is the dividend to start with, since you would factorize the common x from the original polynomial.

I did not complete the whole process for you. I only explained how to start.