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Question

If α,β are real and distinct roots of ax2+bxc=0 and p,q are real and distinct roots of ax2+bx|c|=0, where (a>0), then

A
α,β(p,q)
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B
α,β[p,q]
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C
p,q(α,β)
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D
None of these
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Solution

The correct option is A α,β[p,q]
α,β are real and distinct roots of ax2+bxc=0.
Assume α<β
Therefore,
α,β=b±b2+4ac2a
p, q be real and distinct roots of ax2+bx|c|=0.
Assume p<q
Therefore,
p,q=b±b2+4a|c|2a
Now, c|c|
4ac4a|c|
b2+4acb2+4a|c|
b+b2+4acb+b2+4a|c|
b+b2+4ac2ab+b2+4a|c|2a
βq
Also, b2+4acb2+4a|c|
bb2+4acbb2+4a|c|
bb2+4ac2abb2+4a|c|2a
αp
Hence, α,β[p,q].

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