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Let alpha,beta be real and z be a comple...

Let `alpha,beta` be real and z be a complex number. If `z^2+alphaz""+beta=""0` has two distinct roots on the line Re `z""=""1` , then it is necessary that : (1) `b"" in (0,""1)` (2) `b"" in (-1,""0)` (3) `|b|""=""1` (4) `b"" in (1,oo)`

A

` beta in ( 1 , oo ) `

B

` beta in ( 0 , 1 )`

C

` beta in (-1, 0 ) `

D

`|beta | = 1 `

Text Solution

Verified by Experts

The correct Answer is:
A

Let the roots of the given equation be 1+ ip and 1-ip, where `p in R`
`rArr beta `= product of roots
`= (1+ip)( 1-ip) = 1 p^(2) gt 1 AA p in R`
` rArr beta in (1, oo)`
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