MathDB
Quartic polynomial

Source: Baltic Way 1992 #10

February 17, 2009
algebrapolynomialalgebra proposed

Problem Statement

Find all fourth degree polynomial p(x) p(x) such that the following four conditions are satisfied: (i) p(x)\equal{}p(\minus{}x) for all x x, (ii) p(x)0 p(x)\ge0 for all x x, (iii) p(0)\equal{}1 (iv) p(x) p(x) has exactly two local minimum points x1 x_1 and x2 x_2 such that |x_1\minus{}x_2|\equal{}2.