If every pair from among the equations `x^2+px+qr=0,x^2+qx+rp=0 and x^2+rx+pq` has a common root then the product of three common root is (A) pqr (B) 2pqr (C) `p^2q^2r^2`(D) none of these

Explanation

Let `alpha, beta` are the roots of `x^2+px+qr = 0.`

Then, `alphabeta = qr ->(1)`

Let `beta, gamma` are the roots of `x^2+qx+rp = 0.`

Then, `betagamma = rp ->(2)`

Let `gamma, alpha` are the roots of `x^2+rx+pq = 0.`

Then, `gammaalpha= pq ->(3)`

Multiplying (1),(2) and (3),

`=> (alphabetagamma)^2 = (pqr)^2`

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