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Complex Numbers question

2011 · Shift 0 · Q33
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  5. /2011 · Shift 0 · Q33

Complex Numbers question

2011 · Shift 0 · Q33

JEE MainMathematicsComplex NumbersMCQ+4 / −1
Let α ,β\alpha \,,\betaα,β be real and z be a complex number. If z2+αz+β=0{z^2} + \alpha z + \beta = 0z2+αz+β=0 has two distinct roots on the line Re z = 1, then it is necessary that :
  1. A
    β ∈(−1,0)\beta \, \in ( - 1,0)β∈(−1,0)
  2. B
    ∣β ∣=1\left| {\beta \,} \right| = 1∣β∣=1
  3. C
    β ∈(1,∞)\beta \, \in (1,\infty )β∈(1,∞)
  4. D
    β ∈(0,1)\beta \, \in (0,1)β∈(0,1)
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