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Question
If every pair of the equations x2+px+qr=0 , x2+qx+rp=0 , x2+rx+pq=0 have a common root, then the sum of three common roots is
If every pair of the equations x2+px+qr=0 , x2+qx+rp=0 , x2+rx+pq=0 have a common root, then the sum of three common roots is
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Solution
The correct option is A −(p+q+r)2
Let the roots be α, β; β, γ and γ, α respectively.
∴ α + β = -p, β + γ = -q, γ + α = -r
Adding all, we get ∑α = −(p+q+r)2 etc.
−(p+q+r)2
Let the roots be α, β; β, γ and γ, α respectively.
∴ α + β = -p, β + γ = -q, γ + α = -r
Adding all, we get ∑α = −(p+q+r)2 etc.
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