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There are two ${\bf positive}$ integers $c$ for which the equation

$$5x^2+11x+c=0$$

has rational solutions. What is the product of those two values of $c$?

 Feb 22, 2021
 #1
avatar+118069 
+1

(5x + 1) ( x + 2)  =   5x^2  + 11x   +  2

(5x + 6 ) ( x + 1) =   5x^2  + 11x   +  6

 

Note  that  if the  disriminant is a perfect squarem we  will have rational solutions

 

So

b^2  -    4 * a * c 

11^2   -  4* 5* 2  =    121  -  40  =   81     c  =   2

11^2   -  4 *5 * 6  =   121  - 120 =   1      c  =   6 ........just as we found  !!!!

 

The product   is   12

 

cool cool cool

 

 

 Feb 22, 2021
edited by CPhill  Feb 22, 2021

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