+0  
 
0
923
1
avatar

Find all positive integer values of $c$ such that the equation $x^2-7x+c=0$ only has roots that are real and rational. Express them in decreasing order, separated by commas.

 Jan 23, 2018
 #1
avatar+111331 
+1

x^2  - 7x + c  =  0

 

If tthe roots are real then  this  must be true

 

(-7)^2  - 4c  > 0

 

49  - 4c  >  0

 

49 > 4c

 

49/4  > c

 

The positive integer  values that make this true  are   c = 1 - 12,  inclusive

 

But....for  rational solutions

 

49 - 4c    must be a perfect square

 

So...the integer values that satisfy this are

 

c  = 12, 10, 6

 

 

cool cool cool

 Jan 23, 2018

12 Online Users

avatar
avatar
avatar