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September 5th, 2015, 02:35 AM   #1
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Intermediate Value Theorem

The question attached below. I tried to solve it with piecewise linear function but I still can't. Can someone help me?
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September 11th, 2015, 06:05 PM   #2
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Pn(x)-c=0 has precisely n solutions. Pn(x) is a polyhomial.
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September 11th, 2015, 09:41 PM   #3
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That's only true for one $c$ per function though (well, it may be more, but not all $c$).

I would look at functions like ${1 \over x-a} + {1 \over x-b} + {1 \over x-c}$.
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September 12th, 2015, 03:47 AM   #4
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(x-x1)(x-x2)(x-x3)=0
x3=-c/x1x2
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