Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m.

Guest Apr 13, 2022

#1**+2 **

"Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m."

For the last term to be an integer we must have m - 2 = 1, so m = 3; or m - 2 = 19, so m = 21

Hence sum = 3 + 21 = 24

Kakashi Apr 13, 2022

#2**+1 **

Thanks Kakahi,

I just want to look for myself

Given that m - 2 is a positive integer that divides 3m^2 - 2m + 11, find the sum of all such values of m.

f(m)=3m^2 - 2m + 11

f(2)=12-4+11 = 19 that is the remainder/

19 is prime

19/(m-2) must be a whole number

m-2=19 or m-2=1

m=21 or m=3

Just like Kakashi said :)

Melody Apr 14, 2022