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Let alpha and beta be real and z be a co...

Let `alpha` and `beta` be real and z be a complex number. If `z^(2)+az+beta=0` has two distinct roots on the line Re(z)=1, then it is necessary that

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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