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

Options

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`

Explanation

`:' 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|`