Let `alpha,beta`be real and z be a complex number. If `z^2+alphaz""+beta=""0`has two distinct roots on theline 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 `

Let `alpha,beta`be real and z be a complex number. If `z^2+alphaz""+be

1.	Let `alpha,beta`be real and z be a complex number. If `z^2+alphaz""+beta=""0`has two distinct roots on theline 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 `
Answer» Correct Answer - 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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