Determine the coefficients
Source: Vietnam NMO 1988 Problem 2
February 2, 2009
algebrapolynomialalgebra unsolved
Problem Statement
Suppose P(x) \equal{} a_nx^n\plus{}\cdots\plus{}a_1x\plus{}a_0 be a real polynomial of degree with a_n \equal{} 1, a_{n\minus{}1} \equal{} \minus{}n, a_{n\minus{}2} \equal{}\frac{n^2 \minus{} n}{2} such that all the roots of are real. Determine the coefficients .