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Question

If x2+bxa=0 and x2ax+b=0 have only one common root, then

A
a+b=0
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B
ab=1
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C
a=b
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D
a+b=1
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Solution

The correct option is B ab=1
Given equations x2+bxa=0 and x2ax+b=0

Let the common root be α, then
α2+bαa=0α2aα+b=0
On subtracting, we get
α(b+a)(a+b)=0
(a+b)(α1)=0
a+b=0 or α=1

When a+b=0a=b, then both equation becomes
x2+bx+b=0 and x2+bx+b=0
They are same equation, so both roots is same, so rejecting a+b=0

When α=1, we get
1+ba=0ab=1

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