If $\alpha,\beta $ are real and $z$ is complex number and $z^2+\alpha z +\beta=0$ has two distinct roots on the line $R_e z=1,$ then the values of $\beta$=?

Question

(A) $\beta\in (0,1)$ (B) $\beta\in (-1,0)$ (C) $\beta\in (1,\infty)$ (D) $\beta\in (-1,1)$