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Let alpha, beta (a lt b) be the roots of...

Let `alpha`, `beta (a lt b)` be the roots of the equation `ax^(2)+bx+c=0`. If `lim_(xtom) (|ax^(2)+bx+c|)/(ax^(2)+bx+c)=1` then

A

`(|a|)/(a)=-1`, `m lt alpha`

B

`a gt 0`, `alpha lt m lt beta`

C

`(|a|)/(a)=1`, `m gt beta`

D

`a lt 0`, `m gt beta`

Text Solution

Verified by Experts

The correct Answer is:
C
`(c )` According to the given condition, we have
`|am^(2)+bm+c|=am^(2)+bm+c`
i.e., `am^(2)+bm+c gt 0`
`implies` if `a lt 0` , then `m` lies in `(alpha,beta)`
and if `a gt 0`, then `m` does not lie in `(alpha,beta)`
Hence, option `(c )` is correct, since
`(|a|)/(a)=1impliesa gt 0` and in that case `m` does not lie in `(alpha,beta)`.
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