MathDB

We are given a real number

a

, not equal to

0

1

. Sacho and Deni play the following game. First is Sasho and then Deni and so on (they take turns). On each turn, a player changes one of the “*” symbols in the equation:

*x^4+*x^3+*x^2+*x^1+*=0

with a number of the type

a^n

, where

n

is a whole number. Sasho wins if at the end the equation has no real roots, Deni wins otherwise. Determine (in term of

a

) who has a winning strategy

Problem Statement