Questions
If every pair from among the equations has a common root, then
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=abcSimilar Questions
If the equation and have a common root, then
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