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Find the product of all positive integer values of c such that 8x^2+15x+c=6x^2+7x has two real roots.

 Apr 25, 2022
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Rearrange as

 

2x^2 + 8x  +  c  =  0

 

 

This will have two real roots  when the discriminant  >  0    .......so

 

8^2   -  4 (2) c  >  0

 

64   > 8c

 

64 / 8  >  c

 

So

 

c  <  8

 

So......   seven positive integer values of c  will  work 

 

The product of  these =  7!  =  5040

 

cool cool cool

 Apr 25, 2022

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