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There exist two positive integers c such that the equation

5x^2 + 11x + c = 0

has rational solutions.  Find the product of these two values of c.

 Aug 22, 2021
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There exist two positive integers c such that the equation

5x^2 + 11x + c = 0

has rational solutions.  Find the product of these two values of c.     

 

5x2 + 11x + c = 0  

 

5x2 + 11x + 2 will factor to (5x + 1)(x + 2) .... in this case, then c = 2  

 

5x2 + 11x + 6 will factor to (5x + 6)(x + 1) .... in this case, then c = 6  

 

When you multiply 2 • 6 the product is 12.  

.

 Aug 23, 2021

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