Problem 17 (2019 AMC 12A)
AMC 12AHard
From module Newton's Sums
Problem
Let Sk denote the sum of the kth powers of the roots of the polynomial x³ + ax² + bx + c. In particular, S₁ = -a, S₂ = a² - 2b, and S₃ = -a³ + 3ab - 3c. Let a, b, c be real numbers such that for k = 1, 2, 3, Sk = 3^k. What is a + b + c?