Question

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?

Accepted Answer

C. Product of roots of one equation is 35. Since roots are positive integers, the pair is either $(5, 7)$ or $(1, 35)$. Case 1: Roots are $5, 7$ and $C$. $5 + 7 + C = 41 \implies C = 29$. The roots are $5, 7, 29$. Case 2: Roots are $1, 35$ and $C$. $1 + 35 + C = 41 \implies C = 5$. The roots are $1, 35, 5$. In both cases, 5 is always one of the three roots.

Quadratic Equations and Common Roots

Explanation

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