+0  
 
0
68
2
avatar+160 

Find the product of all positive integer values of c such that 3x^2+7x+c=0 has two real roots.

ANotSmartPerson  Oct 5, 2018
 #1
avatar+92890 
+4

3x^2 + 7x  + c  = 0

 

If this has  2 real roots, the discriminant  [ 7^2 - 4(3)c ] is > 0

 

So

 

49 - 12c   >  0

 

49 > 12c

 

49/12  > c  means the same thing as

 

c < 49/12 

 

c < 4 + 1/12

 

And since  c must be a positive integer value then the possibilities for c  are given by

 

0 < c < 4 + 1/12

 

So....c  = 1, 2, 3, 4

 

And the product of these  =  24

 

 

 

cool cool cool

CPhill  Oct 5, 2018
 #2
avatar+160 
+1

Thanks for helping

ANotSmartPerson  Oct 5, 2018

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