Let $T$ be a tree with an irreducible characteristic polynomial $φ(x)$ over $\mathbb{Q}$. Let $Δ(T)$ be the discriminant of $φ(x)$. It is proved that if $2^{-\frac n2}\sqrt{Δ(T)}$ (which is always an integer) is odd and square free, then every signed tree with underlying graph $T$ is determined by its generalized spectrum.