+147 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 $c$?
+129849 (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
