Official solution
ax2 + bx + c = 0
a, b, c \[ \in \] {1,2,3,4,5,6}
n(s) = 6 \times 6 \times 6 = 216
For equal roots, D = 0 \[ \Rightarrow \] b2 = 4ac
\[ \Rightarrow \] ac = \[{{{b^2}} \over 4}\]
Favourable case :
If b = 2, ac = 1 \[ \Rightarrow \] a = 1, c = 1
If b = 4, ac = 4 :
a = 1, c = 4
a = 4, c = 1
a = 2, c = 2
If b = 6, ac = 9 \[ \Rightarrow \] a = 3, c = 3
\[ \therefore \] Favorable cases = 5
\[ \therefore \] Required probability = \[{5 \over {216}}\]