If `alphaa n dbeta(alpha<beta)` are the roots of the equation `x^2+b x-c=0,w h e r eb<0<c ,` then `0<alpha<beta` b. `alpha<0<beta<|alpha|` c. `alpha<b

Question

If `alphaa n dbeta(alphaA. `0lt alpha lt beta`
B. alpha lt 0lt betalt|alpha|`
C. `alpha lt beta lt 0`
D. `alphalt 0lt|alpha|lt beta`

Answer 1

Correct Answer - B
Given `cle 0lt b`
Since, `alpha+beta=-b" "…(i)`
and `alpha beta=c" "…(ii)`
From Eq. (ii), `c lt 0implies alpha betagt0`
`implies` Either `alpha` is-ve or `alpha` is + ve, `beta` is - ve. From Eq. (i), `b gt 0 impliesalpha+beta 0implies` ths sum is negative.
`implies` Modulus of negative quantity is `gt` modulus of positive quantity but `alpha lt beta` is given.
Therefore it is clear that `alpha` is negative and `beta` is positive and modulus of `alpha` is greater than modulus of `beta`
`implies alpha lt 0 lt beta lt |alpha|`
Note This question is not on hte theory of interval in whihc root lie, which appears looking as first sight. it is new type and first time asked in the paper it is imprtant for future. The actual type is interval in which parameter lie.