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# If every pair from among the equations  has a common root, then

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a
the sum of the three common roots is -12 (a + b + c)
b
the sum of the three common roots is 2(a + b + c)
c
one of the values of the product of the three common roots is abc
d
the product of the three common roots is a2b2C2
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detailed solution

Correct option is A

Since each pair has common root, let the roots be α,β forEq. (1): β,γ for Eq.(2) and γ,α for Eq. (3). Therefore,α+β=−a,αβ=bcβ+γ=−b,βγ=caγ+α=−c,γα=abAdding, we get2(α+β+γ)=−(a+b+c)⇒ α+β+γ=−12(a+b+c)Also by multiplying product of roots, we haveα2β2γ2=a2b2c2 or αβγ=abc

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