First, you should realize this is incorrect because they are asking for an "integer" value. Second, if b^2-4ac < 0 (a neg. #), then you have an imaginery root. This implies that
b^2 < 4ac. Then plug in what you know! Then
16 < 4(3)c. Following along, this yields 16/12 < c or c > 4/3. The smallest integer greater that 4/3 is 2. So, 2 is your answer!