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MathNet 2009-part-01 — 175 problems (EN–VI) Question 33

Math Olympiad Vault · MathNet 2009-part-01 — 175 problems (EN–VI)

Question 33

About a monic polynomial $p(x)$ of degree $n \ge 2$ is known that all its complex roots $\alpha$ are real and satisfy $\alpha \le 1$ and that $p(2) = 3^n$. Which values can $p(1)$ have?

(A monic polynomial $p(x)$ of degree $n$ is one whose coefficient of $x^n$ is equal to one.)