What is the reciprocal sum of the roots for the equation $\dfrac{2}{3}x^{2}- \dfrac{1}{3}x = 0$?

For the quadratic equation (2/3)x^2 - (1/3)x = 0, we identify a = 2/3 and b = -1/3. The sum of the roots is -b/a = -(-1/3) / (2/3) = 1/2. The reciprocal sum of the roots is calculated by dividing the sum of the roots by the product of the roots, using the formula (-b/a) / (c/a), which simplifies to -b/c. Here, -(-1/3) / 0 equals infinity, but using the relation that 1/x1 + 1/x2 = (x1 + x2) / (x1 * x2), one root is 0 and the other is 1/2, making the reciprocal sum -(-1/3) / (2/3) = 2 based on the -a/b formula; the value is 2.

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