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Q.

If each pair of the equation x2+ax+b=0,x2+bx+c=0 and x2+cx+a=0 has a common root, then product of all common roots is

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a

abc

b

2abc

c

ab+bc+ca

d

2ab+bc+ca

answer is A.

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Detailed Solution

Let the roots be α,β,β,γ and γ,α then,αβ=b, βγ=c and γα=a⇒αβγ=abc

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If each pair of the equation x2+ax+b=0,x2+bx+c=0 and x2+cx+a=0 has a common root, then product of all common roots is