If alpha,beta are the roots x^2+px+q=0 a...

If `alpha,beta` are the roots `x^2+px+q`=0 and `gamma,delta` are the roots of `x^2+rx+s`=0, evaluate `(alpha-gamma)(alpha-delta)(beta-gamma)(beta-delta)` in terms of p,q,r and s. Deduce the condition that the equation may have a common root.

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