Let $\alpha, \beta$ be real and $z$ be a complex number. If $z^2 + \alpha z + \beta = 0$ has two distinct roots on the line $Rez=1$, then it is necessary that

Question

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