Explanation

Let the roots be r and 2r. Then 3r = −(3a−1)/(a²−5a+3) and 2r² = 2/(a²−5a+3), so r² = 1/(a²−5a+3). Squaring the sum relation: 9/(a²−5a+3) = (3a−1)²/(a²−5a+3)², i.e. 9(a²−5a+3) = 9a²−6a+1. This reduces to −45a + 27 = −6a + 1, so 39a = 26 and a = 2/3: option A. The negative options fail the sign check.