Q.

If every pair from among the equations x2+ax+bc=0, x2+bx+ca=0, and x2+cx+ab=0 has a common root, then

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By Expert Faculty of Sri Chaitanya

the sum of the three common roots is -12 (a + b + c)

the sum of the three common roots is 2(a + b + c)

one of the values of the product of the three common roots is abc

the product of the three common roots is a2b2C2

answer is 1,3.

(Detailed Solution Below)

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Detailed Solution

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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