**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**