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Question
lf every pair from among the equations x2+ax+bc=0, x2+bx+ca=0 and x2+cx+ab=0 has common root, then the sum of the three common roots is
lf every pair from among the equations x2+ax+bc=0, x2+bx+ca=0 and x2+cx+ab=0 has common root, then the sum of the three common roots is
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Solution
The correct option is C −(a+b+c)2
Let (α,β),(β,r),(r,α) be the roots respectively .
Then, α+β=−a;β+r=−b;r+α=−c
α+β+β+r+r+α=−(a+b+c)
α+β+r=−(a+b+c)2
Let (α,β),(β,r),(r,α) be the roots respectively .
Then, α+β=−a;β+r=−b;r+α=−c
α+β+β+r+r+α=−(a+b+c)
α+β+r=−(a+b+c)2
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