Find all positive integer values of c such that the equation x^2 - 11x + c = 0 only has roots that are real and rational. Express them in decreasing order, separated by commas.
+36915 Real and rational maeans the discriminant of this quadrtatic must be > 0
b^2 - 4ac >0
112 - 4 (1)(c) >0
121>4c
4c<121
c< 30.25 I 'll let you make the list 30,29,........1
+36915 Sorry.... some of those results will be irrational (I was thinking 'imaginary')....so ...
121 - 4c = rational
30,24,18,10 I think are the ones that will result in a perfect square discriminant
example 121 - 4(18) = 49 a perfect square
