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

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