What are the integer values for x if you want this equation: | 4x^2 - 12x -27 | to be a prime number.

hearts123 Feb 2, 2019

#1**+3 **

This is my best attempt :

l 4x^2 - 12x -27 l can be factored as

l (2x - 9) (2x + 3 ) l =

l 2x - 9 l * l 2x + 3 l

To be prime either the first factor must possibly be 1 or -1 or the same for the second factor

So

2x - 9 = 1 means that x = 5 and 2(5)+ 3 = 13....so this value for x generates a prime

2x - 9 = - 1 means that x = 4 and 2(4) + 3 = 11.....so this value for x geherates a prime

Also

2x + 3 = 1 means that x = -1 and 2(-1) - 9 = - 7 ...but l -7l = 7....so this value for x generates a prime

2x + 3 = -1 means that x = -2 and 2(-2) - 9 = -5 ...but l -5 l = 5...so this value for x generates a prime

So I find four integer values for x ⇒ { -2, -1, 4 , 5 }

CPhill Feb 2, 2019