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 and the product of roots of \(p(x)\) is 1.

Image Credit: Wikimedia Septic Graph

Problem Loading...

Note Loading...

Set Loading...