Two different quadratic equations have a common root. Let th

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Two different quadratic equations have a common root. Let the three unique roots of the two equations be A, B and C - all of them are positive integers. If (A + B + C) = 41 and the product of the roots of one of the equations is 35, which of the following options is definitely correct?

[MBA XAT 2018]

A The common root is 29.

B The smallest among the roots is 1.

C One of the roots is 5.

D Product of the roots of the other equation is 5.

E All of the above are possible, but none are definitely correct.