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 Re z = 1, then it is necessary that :
$\beta \, \in ( - 1,0)$
$\left| {\beta \,} \right| = 1$
$\beta \, \in (1,\infty )$
$\beta \, \in (0,1)$
Solution
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