Polynomial phobia abandoned!

Algebra Level 4

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 \(x^{17}\) is 1.

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

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