Trees with two eigenvalues?

Question

Is it possible for a tree of order $n$ ($n$ even) to have eigenvalues $(\lambda_1, \ldots, \lambda_1, -\lambda_1, \ldots, -\lambda_1)$ ? Or perhaps $(\lambda_1, \ldots, \lambda_1, 0,-\lambda_1, \ldots, -\lambda_1)$ if $n$ is odd ?

Thanks.