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Find the product of all positive integer values of c such that  \(8x^2+15x+c=0\) has two real roots.

Guest Jan 1, 2018
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8x^2  +  15x   + c  =   0

 

This will nave two real  roots if

 

15^2  -  4 * 8 * c  >  0

 

225  -  32c  >  0

 

225  >  32c

 

225/ 32  > c

 

7.03125  > c

 

So......c will have two real roots  [and  be positive ]   for  all  integer values  from 1 to 7, inclusive

 

And the procuct of these possible values for c   =  7!   =  5040

 

 

 

cool cool cool

CPhill  Jan 2, 2018

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