1. The problem statement, all variables and given/known data Let k be a constant. If α and β are the roots of the equation 3x^2 + 2x - k = 0, find the value of 3α^2 - 2β in terms of k. 2. Relevant equations 3. The attempt at a solution Obviously, the usual αβ = -k/3 α + β = -2/3 has been written but I couldn't put them into the equation required despite a full hour's effort. Also, tried writing (-b+-sqrt(b^2-4ac))/2a, and put respective roots into the equation, it yields something similar to the provided solution, but has an extra root term. The solution is 4/3 + k. The latter method gets 4/3 + k + sqrt(4+12k)/6.