If the roots of the equation $a{x^2} + bx + c = 0$ are of the form $\displaystyle {{K + 1} \over K}$ and $\displaystyle{{K + 2} \over {K + 1}}$ then sum of roots is equal to;

Let the roots be r = (K + 1)/K = 1 + 1/K and s = (K + 2)/(K + 1) = 1 + 1/(K + 1). Multiplying the roots gives rs = (1 + 1/K)(1 + 1/(K + 1)) = (K + 1)/K * (K + 2)/(K + 1) = (K + 2)/K = 1 + 2/K. Using the relation between roots and coefficients for the quadratic equation, rs = c/a. Since the product depends on the unknown variable K, it cannot be expressed solely in terms of a, b, and c. Therefore, none of the provided options match.

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