+0  
 
-1
15
1
avatar+624 

What is the greatest integer $x$ such that $|6x^2-47x+15-28x|$ is prime?

 

I think you use factorization here, but I don't know how.

 Sep 6, 2023
 #1
avatar+128732 
+1

I don't believe that an integer  exists to  make this prime

 

Simplifying  we have

 

l 6x^2 - 75x  + 15 l

 

l 3 ( 2x^2  - 25x + 5) l

 

3 l 2x^2 -25x + 5 l

 

The only way this  can  be  prime is  if the expression   in the absolute  value  bars  is  either = 1  or  = -1

 

2x^2 - 25x + 5  = 1

 

2x^2  - 25x + 4 =  0 

 

Using the Q formula  x is   not an integer  because  the discrminant = 25^2 - 4(2)*(4)  = 593 which is  not  a perfect square

 

Likewise

 

2x^2 - 25x + 5 =   -1

 

2x^2 - 25x + 6  =  0

 

The discriminant = 25^2 - 4* 2 * 5  =   585  which is also not a  perfect square

 

 

cool cool cool

 Sep 6, 2023

2 Online Users