Uniform number of distinct roots
Source: 2017 Korean Winter Program Practice Test 1 Day 1 #3
January 18, 2017
algebrapolynomial
Problem Statement
Do there exist polynomials , with real coefficients and a positive integer satisfying the following condition? (Here, the equation is considered to have distinct real roots. The equation has infinitely many distinct real roots.) For any real numbers with , the number of distinct real roots of is .