Let α,β be real and z complex. If z²+α z+β=0 has two distinct roots on the line Rez=1, then it is necessary that (a) β∈(-1,0) (b) |β|=1 (c) β∈(1,∞) (d) β∈(0,1)

Correct answer: (c) β∈(1,∞) Distinct roots on Rez=1 must be conjugates 1± it (t 0), so β= product =1+t²>1, i.e. β∈(1,∞). JEE Main 2011 · Complex Numbers — verified solution by the Vidaara Team.

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[JEE Main 2011] let alpha beta be real and z complex if z 2 alpha z beta

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

(a) $\beta\in(-1,0)$
(b) $|\beta|=1$
(c) $\beta\in(1,\infty)$
(d) $\beta\in(0,1)$

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (c) $\beta\in(1,\infty)$

Distinct roots on $\operatorname{Re}z=1$ must be conjugates $1\pm it$ ($t\ne0$), so $\beta=$ product $=1+t^2>1$, i.e. $\beta\in(1,\infty)$.

JEE Main 2011 · Complex Numbers — verified solution by the Vidaara Team.

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