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Question

If x2+ax+b=0 and x2+bx+a=0 have a common root, then

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

The correct option is B a=b
Let α be the common root.
α2+aα+b=0 ...(1)
and α2+bα+a=0 ...(2)
Solving (1) and (2), we get,
α2a2b2=αba=1ba
α2=a2b2ba, α=1
a2b2ba=1
a2b2=ba
(ab)(a+b+1)=0
ab=0 or a+b+1=0

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