text: kx^2 - 5x + 3 = 0\nSince you don't have any criteria listed, then k can be anything.  That is, there is no limit on k.\n\nHowever, I'm assuming that the problem states that you need real roots.\nLook at the discriminant.\ndiscriminant = b^2 - 4ac\na = k, b = -5 and c = 3\nb^2 - 4ac\n= (-5)^2 - 4(k)(3)\n= 25 - 12k\nIn order to have real roots, the discriminant must be greater than or equal to zero.\n25 - 12k >= 0\n25 > = 12k\n25/12 >= k\nor k <= 25/12 or k <= 2 &1/25\nThe largest integer that is less than or equal to 25/12 is 2.