Is problem not true? When f(-1)=0 then the problem is false.

the correct version of this problem is: $ \alpha, \beta, \gamma$ are positive integers, 0, $ \alpha \beta, \beta\gamma, \gamma\alpha$ are the roots of a polynomial f(x) with degree 4 and the coefficient of the first term is 1. If there exists an integer such that $ f(-1)=f^2(s)$, Prove that $ \alpha \beta$ is not a perfect square.

It follows from here