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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.

 Jul 16, 2019
 #1
avatar+103999 
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If this has two real roots, then  the discriminant must be > 0

 

So

 

15^2  - 4(8)c >  0

 

225 - 32c >  0

 

225 > 32c

 

c < 225/32  ⇒ c  <  7.03125

 

So....the positive integer values for c  that produce two real roots are  [ 1, 7 ]  

 

And their product  = 7!   =  5040

 

cool cool cool

 Jul 16, 2019
edited by CPhill  Jul 16, 2019

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