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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a

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

b

The product of the three common roots is abc

c

The product of the three common roots is a2b2c2

d

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

answer is A, C.

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Detailed Solution

α+β=a    αβ=bc      β+γ=bβγ=ca          γ+α=c    γα=ab2(α+β+γ)=(a+bc);    α2β2γ2=a2b2c2α+β+γ=12(a+bc);    αβγ=abc

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