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Question

If every pair among the equations x2+px+qr=0, x2+qx+rp=0 and x2+rx+pq=0 have a common root, then (sumofroots)(productofroots) =


A

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B

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C

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D

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Solution

The correct option is C


x2+qx+rp=0 ; α,β

x2+px+rq=0 ; β,γ

x2+rx+pq=0 ; γ,α

Then, β2+qβ+rp=0,β2+pβ+qr=0

(qp)β = r(q-p) β = r.

Similarly , γ=q,α=p .

(α+β+γ)αβγ = (p+q+r)pqr .


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