# 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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