Home > Algebra, Olympiad, Problem Solving > IMC 2014 Day 1 Problem 3

## IMC 2014 Day 1 Problem 3

Let ${n}$ be a positive integer. Show that there are positive real numbers ${a_0,a_1,...,a_n}$ such that for each choice of signs the polynomial

$\displaystyle \pm a_nx^n\pm a_{n-1}x^{n-1}\pm ... \pm a_1x\pm a_0$

has ${n}$ distinct real roots.

IMC 2014 Day 1 Problem 3