text: find the largest integral value of k in kx squared  - 5x + 3=0?   kx^2 - 5x + 3 = 0 since you don't have any criteria listed, then k can be anything.  that is, there is no limit on k.  however, i'm assuming that the problem states that you need real roots. look at the discriminant. discriminant = b^2 - 4ac a = k, b = -5 and c = 3 b^2 - 4ac = (-5)^2 - 4(k)(3) = 25 - 12k in order to have real roots, the discriminant must be greater than or equal to zero. 25 - 12k >= 0 25 > = 12k 25/12 >= k or k <= 25/12 or k <= 2 &1/25 the largest integer that is less than or equal to 25/12 is 2.