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Polynomial phobia abandoned! (Posted on 20190414) 

What is the minimum value of p(2) if the following 4 conditions are followed?
1) p(x) is a polynomial of degree 17.
2) All roots of p(x) are real.
3) All coefficients are positive.
4) The coefficient of x^{} is 1.
5) The product of roots of p(x) is 1.
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