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Find the product of all positive integer values of c such that 3x^2 + 17x + c has two real roots.

 Jun 23, 2022
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3x^2 + 17x +  c

 

If we have two real roots, the discriminant is >  0 

 

So

 

17^2  -  4 * 3 * c   >  0

 

289  >    12c

 

289 / 12  > c

 

Which implies that

 

0 > c > 289/12                 where c is an integer

 

0 > c <  24+ 1/12

 

The product of all integer c's  that make this true  =  24!  = 620448401733239439360000

 

 

cool cool cool

 Jun 23, 2022

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