To get a double root, you need the discriminant of the quadratic formula to be zero.
Discriminant: b2 - 4·a·c
Quadratic: 2x2 + 3x + k ---> a = 2 b = 3 c = k
---> b2 - 4·a·c = 0 ---> 32 - 4·2·k = 0 ---> 9 - 8k = 0
You'll need to solve this equation for k.
+4 
