Final answer:
The value of k in the given quadratic equation cannot be determined with the information provided, as we need the specific values of the roots x1 and x2 to apply Vieta's formulas and calculate the product of the roots.
Step-by-step explanation:
The student's question pertains to finding the value of k in the quadratic equation 3x^2 − 2x − k = 0. To determine the value of k, we need to apply the relationship between the coefficients of a quadratic equation and its roots. According to Vieta's formulas, for a quadratic equation of the form ax^2 + bx + c = 0, where x_1 and x_2 are the roots, the sum of the roots is −b/a, and the product of the roots is c/a.
Given the original equation, a = 3, b = −2, and c = −k. The sum of the roots is thus 2/3, and the product of the roots is −k/3. Without the specific values for x_1 and x_2, we cannot find a single solution for k. However, we can infer that there might be a typo in the provided question since k is part of the equation to solve. If the question intended to ask for the product of the roots given that x_1 and x_2 are known, then we could calculate k. Nevertheless, among the given options, without additional information or context to indicate the values of the roots, we cannot confidently determine the value of k.