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If alpha and beta(alpha lt beta) are the...

If `alpha` and `beta(alpha lt beta)` are the roots of the equation `x^(2)+bx+c=0` where `c lt 0ltb`, then

A

`|alpha|=|beta|, |alpha| gt 1`

B

`|alpha| ge 1`

C

`|beta| lt 1`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
It is given that the roots are imaginary. Therefore, `b^(2) - 4ac lt 0`. The roots `alpha and beta` are given by `alpha =(-b+i sqrt(4ac -b^(2)))/(2a) and beta=(-b -i sqrt(4ac - b^(2)))/(2a)`
Clearly, `alpha = bar (beta)`. Therefore, `|alpha|=|bet|`.
Further more, `|alpha|=sqrt((b^(2))/(4a^(2))+(4ac-b^(2))/(4a^(2)))=sqrt((c)/(a)) rArr |alpha| gt 1" "[because c gt a]`
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