Ten $x^2 +px+q$
Source: All-Russian Olympiad 1996, Grade 10, Second Day, Problem 8
April 18, 2013
quadraticsalgebra proposedalgebra
Problem Statement
Goodnik writes 10 numbers on the board, then Nogoodnik writes 10 more numbers, all 20 of the numbers being positive and distinct. Can Goodnik choose his 10 numbers so that no matter what Nogoodnik writes, he can form 10 quadratic trinomials of the form , whose coeficients and run through all of the numbers written, such that the real roots of these trinomials comprise exactly 11 values?I. Rubanov