SOLUTION: at what time is your roller coaster at ground level with a polynomial value of x^5-4x^4-7x^3+14x^2-44x+120 and also the breakdown to the exact value of the roots

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Question 1129726: at what time is your roller coaster at ground level with a polynomial value of x^5-4x^4-7x^3+14x^2-44x+120 and also the breakdown to the exact value of the roots
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!
breakdown to the exact value of the roots:














the coaster returns to ground level at , , , the three real zeros of the function



Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
at what time is your roller coaster at ground level with a polynomial value of x^5-4x^4-7x^3+14x^2-44x+120 and also the breakdown to the exact value of the roots
Using the RATIONAL ROOT THEOREM, find 2 zeroes. I found 2 zeroes to be 2 and - 3, which results in the 2 factors, (x - 2) and (x + 3). 

FOILing that gives you a trinomial that can be used as the DIVISOR, and with the LONG-DIVISION-of-POLYNOMIALS method, you get yet another trinomial (). 

Using the RATIONAL ROOT THEOREM again will result in a factor (x - 5), and along with LONG-DIVISION-of-POLYNOMIALS method, will result in a binomial (), which

cannot be factored further.

We now get: 

Do you think you can continue from here?

OR

After finding ALL zeroes (there're 3 of them), use each and synthetic division to find the fourth and final factor, and from that, the final zero/solution. 

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