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Question

The roots of the equation (b+c)x2(a+b+c)x+a=0, where a,b,cQ and b+ca, are

A
rational and equal
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B
rational and distinct
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C
irrational and equal
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D
cannot be determined
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Solution

The correct option is B rational and distinct
(b+c)x2(a+b+c)x+a=0
Δ=(a+b+c)24(b+c)a
=a2+b2+c2+2ab+2bc+2ca4ab4ac
=a2+b2+c22ab+2bc2ac
=(abc)2>0 as b+ca
Δ is a perfect square and positive.
Hence, the roots are rational and distinct.

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