Explanation

Let the roots be 3k and 2k. Their product 6k² = 5/12 gives k² = 5/72. Their sum 5k = −m/12; for m > 0 the roots must be negative, so k = −√10/12. Then m = −60k = −60(−√10/12) = 5√10. Hence option (A) 5√(10). (Trap: taking k positive gives m = −5√10, which is rejected since m must be positive.)