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Let o lt p lt q and a ne 0 such that the...

Let `o lt p lt q` and `a ne 0` such that the equation `px^(2) +4 lambda xy +qy^(2) +4a (x+y +1) = 0` represents a pair of straight lines, then a can lie in the interval

A

`(-oo,oo)`

B

`(-oo,p]`

C

`[p,q]`

D

`[q,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B, D
We must have
`p.q.4a +2.2a.2a.2lambda -p.4a^(2) -q.4a^(2)-4a.4lambda^(2) =0`
`rArr 4 lambda^(2) -4a lambda + {(p+q)q-pq} =0 ( :' q ne 0)`
Since, `lambda in R, 16a^(2) - 4.4 {(p+q)a-pq} ge 0`
or `(a-p)(a-p) ge 0`
`:. a le p` or `a ge q`
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