We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
46
1
avatar

Given that m - 2 divides 3m^2 - 2m + 11, find all possible values of m.

 Nov 11, 2019
 #1
avatar+70 
+1

Assuming that m is an integer, we must have \(\frac {3m^2-2m+11} {m-2}=N\), where N is an integer. So since

\(N=\frac{3m^2-2m+11} {m-2}=3m+4+\frac{19} {m-2}\), the fraction\(\frac{19} {m-2}\)must be an integer. But since the numerator of this fraction is prime, its only divisors are \(\pm 1\) and \(\pm19\). So we must have \(m-2=\pm1\) and \(m-2=\pm19\). By solving these equations for m you get four possible values for m. Have fun!

 Nov 11, 2019

6 Online Users

avatar