SOLUTION: do all the roots of the polynomial x^5-4x^4-7x^3+14x^2-44x+120 make sense in regards to a roller coaster engineering project problem.explain why or why not in a complete sentence.

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Question 1129742: do all the roots of the polynomial x^5-4x^4-7x^3+14x^2-44x+120 make sense in regards to a roller coaster engineering project problem.explain why or why not in a complete sentence.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
breakdown to the exact value of the roots:
x%5E5-4x%5E4-7x%5E3%2B14x%5E2-44x%2B120+=0
x%5E5-2x%5E4-2x%5E4-11x%5E3%2B4x%5E3%2B22x%5E2-8x%5E2-60x%2B16x%2B120=0

x%5E4%28x-2%29-11x%5E2%28x-2%29-2x%5E3%28x-2%29-8x%28x-2%29-60%28x%2B2%29=0
%28x-2%29%28x%5E4-2x%5E3-11x%5E2-8x-60%29=0
%28x-2%29%28x%5E4-2x%5E3-15x%5E2%2B4x%5E2-8x-60%29=0
%28x-2%29%28%28x%5E4%2B4x%5E2%29-%282x%5E3%2B8x%29-%2815x%5E2%2B60%29%29=0
%28x-2%29%28x%5E2%28x%5E2%2B4%29-2x%28x%5E2%2B4%29-15%28x%5E2%2B4%29%29=0
%28x-2%29%28x%5E2+%2B+4%29%28x%5E2+-+2+x+-+15%29=0
%28x-2%29%28x%5E2+%2B+4%29%28x%5E2+-+5x%2B3x+-+15%29=0
%28x-2%29%28x%5E2+%2B+4%29%28%28x%5E2+-+5x%29%2B%283x+-+15%29%29=0
%28x-2%29%28x%5E2+%2B+4%29%28x%28x+-+5%29%2B3%28x+-+5%29%29=0
%28x+-+2%29+%28x+%2B+3%29+%28x+-+5%29+%28x%5E2+%2B+4%29=0

the coaster returns to ground level at x+=+2, x=5, x+=+-3, the three real zeros of the function


do all the roots of the polynomial x%5E5-4x%5E4-7x%5E3%2B14x%5E2-44x%2B120 make sense in regards to a roller coaster engineering project problem????

the roots of the polynomial mathematically make sense in regards to a roller coaster engineering project problem because these values (x+=+2, x=5, x+=+-3) mean the ride starts on the ground

but, mathematical end behavior of this function does not make sense++practically


function has local maximum and minimum where first derivative is equal to zero:
and it is 5+x%5E4+-+16+x%5E3+-+21+x%5E2+%2B+28+x+-+44=0 at
x=+-1.89
x=4.03
so, function is
highlight%28Increasing%29 on: (-infinity,-1.89),(4.03,infinity)
highlight%28Decreasing%29 on: (-1.89,4.03)