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.

Guest Oct 25, 2020

#1**+1 **

Real and rational maeans the discriminant of this quadrtatic must be > 0

b^2 - 4ac >0

11^{2} - 4 (1)(c) >0

121>4c

4c<121

c< 30.25 I 'll let you make the list 30,29,........1

ElectricPavlov Oct 25, 2020

#2**0 **

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

ElectricPavlov
Oct 25, 2020