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

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

A

`0 lt alpha lt beta`

B

`alpha lt 0 lt beta lt |alpha|`

C

`alpha lt beta lt 0`

D

`alpha lt 0 lt |alpha|lt beta`

Text Solution

Verified by Experts

`:' alpha+beta=-b, alpha beta=c` …………….i
`:'clt0impliesalpha betalt0`
Let `alpha lt 0, beta gt0`
`:.|alpha|=-alpha` and `alpha lt 0 lt beta[ :' alpha lt beta]`……ii
From Eq. I we get `-|alpha|+beta lt 0`
`impliesbetalt |alpha|`……iii
From Eqs ii and iii we get
`0 lt 0lt betalt |alpha|`
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