Concept: The question tests on the ability to solve questions on Quadratic Equations
Solution:
A quadratic equation of the form ax^2+bx+c=0 has equal roots, when b^2−4ac=0
Here b = 2(m + 1) = 2m + 2, a = 3m + 1 and c = m
Therefore (2m+2)^2−[4∗(3m+1)∗m]=0
4m^2+8m+4−(12m^2+4m)=0
−8m2+4m+4=0
2m^2−m−1=0
2m^2−2m+m−1=0
2m(m - 1) + 1(m - 1) = 0
(m - 1) (2m + 1) = 0
m = 1 or m = -1/2
Option A