Who Wins

Algebra Level 3

A and B play a game,tgey are given a polynomial x^4+()x^3+()x^2+()x+() They have to replace () by a integer in their turn (only one at a time) B starts first and wins if after 4th step the polynomial has no integral roots else A wins. Assuming game goes by perfect strategy who wins?

B A Game ends in a draw

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