jee-main 2011 Q61

jee-main · India Complex Numbers Arithmetic Solving Equations for Unknown Complex Numbers

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
(1) $\beta\in(-1,0)$
(2) $|\beta|=1$
(3) $\beta\in(1,\infty)$
(4) $\beta\in(0,1)$

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\\
(1) $\beta\in(-1,0)$\\
(2) $|\beta|=1$\\
(3) $\beta\in(1,\infty)$\\
(4) $\beta\in(0,1)$

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