A Game of Polynomials
Written on a blackboard is the polynomial \(x^2+x+2014\). Calvin and Peter take turns alternatively (starting with Calvin) in the following game. During his turn, Calvin should either increase or decrease the coefficient of x by 1, and during his turn, Peter should either increase or decrease the constant coefficient by 1. Calvin wins if at any point of time the polynomial on the blackboard at that instant has integer roots. Which of the following is true.