Question 2
Suppose $a_i \gt 0$, $i = 1, \dots, n$. Prove that the polynomial
$$
p(x) = -1 + \sum_{i=1}^{n} a_i x^i
$$
has precisely one positive root.
$$
p(x) = -1 + \sum_{i=1}^{n} a_i x^i
$$
has precisely one positive root.
MathNet 2026 — Part 06 Question 2
Math Olympiad Vault · MathNet 2026 — Part 06