MathDB

125

Part of 1969 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 125 All Soviet Union MO 1969 x^3 + ?x^2 + ?x + ? = 0

Source:

6/23/2019
Given an equation x3+?x2+?x+?=0x^3 + ?x^2 + ?x + ? = 0 First player substitutes an integer on the place of one of the interrogative marks, than the same do the second with one of the two remained marks, and, finally, the first puts the integer instead of the last mark. Explain how can the first provide the existence of three integer roots in the obtained equation. (The roots may coincide.)
Cubicalgebra