x = 2 is a root of given equation substitute x = 2 in L.H.S.
L.H.S. = 3(2)^{2} – 2k × 2 + 2m = 0
12 – 4k + 2m = 0
4k – 2m = 12 …(i)
Similarly when x = 2 is root of given equation
Substitute x = 3 in L.H.S.
L.H.S. = 3(3)^{2} – 2k × 3 + 2m = 0
27 – 6k + 2m = 0
6k – 2m = 27 …(ii)
On solving equations (i) and (ii), we get
k = 15/2 and m = 9