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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.

 Oct 25, 2020
 #1
avatar+28021 
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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

 Oct 25, 2020
 #2
avatar+28021 
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

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