Polynomial phobia abandoned!

Algebra Level 4

What is the minimum value of p(2)p(2) if the following 4 conditions are followed?

  1. p(x)p(x) is a polynomial of degree 1717.

  2. All roots of p(x)p(x) are real.

  3. All coefficients are positive.

  4. The coefficient of x17x^{17} is 1.

  5. The product of roots of p(x)p(x) is -1.

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