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There are two positive integers c for which the equation
5x^2+11x+c=4x^2 + 3x
has rational solutions. What is the product of those two values of c?

 Aug 22, 2021
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There are two positive integers c for which the equation
5x^2+11x+c=4x^2 + 3x
has rational solutions. What is the product of those two values of c?
     

 

Start with                                           5x2 + 11x + c = 4x2 + 3x  

 

Subtract (4x2 + 3x) from both sides      x2 + 8x + c  =  0   

 

If c = 16, then the quadratic will factor to (x + 4)(x + 4)   

If c = 15, then the quadratic will factor to (x + 5)(x + 3)  

If c = 12, then the quadratic will factor to (x + 6)(x + 2)  

If c =  7, then the quadratic will factor to  (x + 7)(x + 1)  

 

The problem says two.  If that means ONLY two, then I'm misunderstanding the problem.     

.

 Aug 22, 2021

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