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Find the product of all positive integer values of c such that 8x^2+15x+c=7x^2+11x has two real roots.

 Jun 7, 2022
 #1
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8x^2  + 15x + c  = 7x^2 + 11x      rearrange as

 

x^2  + 4x  +  c   =  0

 

If we have two real roots the discriminant  is >  0

 

So

 

4^2 - 4(1)(c)  > 0

 

16 >  4c

 

4 > c

 

c < 4

 

So  c =   1, 2  or 3 

 

The product of all possible c's  =  1 * 2 * 3   =  6

 

 

cool cool cool

 Jun 7, 2022

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