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Question

If α and β are the roots of a quadratic equation satisfying the conditons αβ=4 and αα1+ββ1=a27a24,α,β,aR. For what values of a will the quadratic equation have equal roots?

A
3
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B
5
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C
3
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D
5
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Solution

The correct options are
A 3
C 3
α(β1)+β(α1)(α1)(β1)=a27a24

2αβ(α+β)αβ(α+β)+1=a27a24

8(α+β)5(α+β)=a27a24
[αβ=4]

1+35(α+β)=13a24(α+β)=a2+1(1)
For roots to be equal
αβ=4α2=4α=±2
Using equation (1),
2α=a2+1a=±2α1a=±3

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