Quartic polynomial
Source: Baltic Way 1992 #10
February 17, 2009
algebrapolynomialalgebra proposed
Problem Statement
Find all fourth degree polynomial such that the following four conditions are satisfied:
(i) p(x)\equal{}p(\minus{}x) for all ,
(ii) for all ,
(iii) p(0)\equal{}1
(iv) has exactly two local minimum points and such that |x_1\minus{}x_2|\equal{}2.