When a quadratic equation has twin roots, its discriminant #Delta# is equal to zero.
The formula for the discriminant is #Delta = b^(2) - 4 a c#.
Let's evaluate the discriminant of our quadratic equation:
#Rightarrow Delta = (8 - 2 m)^(2) - 4 (1 - m) (12)#
#Rightarrow Delta = 64 - 32 m + 4 m^(2) - 12 (4 - 4 m)#
#Rightarrow Delta = 64 - 32 m + 4 m^(2) - 48 + 48 m#
#Rightarrow Delta = 4 m^(2) + 16 m + 16#
Then, let's set it equal to zero:
#Rightarrow Delta = 0#
#Rightarrow 4 m^(2) + 16 m + 16 = 0#
#Rightarrow 4 (m^(2) + 4 m + 4) = 0#
#Rightarrow m^(2) + 4 m + 4 = 0#
Now, let's factorise the equation using the middle-term break:
#Rightarrow m^(2) + 2 m + 2 m + 4 = 0 #
#Rightarrow m (m + 2) + 2 (m + 2) = 0#
#Rightarrow (m + 2) (m + 2) = 0#
#Rightarrow (m + 2)^(2) = 0#
#Rightarrow m + 2 = 0#
#therefore m = - 2#
