# Polynomial phobia abandoned!

**Algebra**Level 4

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

\(p(x)\) is a polynomial of degree \(17\).

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

All coefficients are positive.

The coefficient of \(x^{17}\) is 1.

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