Let a, b be real and z be a complex number. If z 2 + az + b = 0 has two distinct roots on the line Re z =1, then it is necessary that :

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 $\operatorname{Re} z=1$, then it is necessary that: