The coefficients a, b and c of the quadratic equation,

$a x^{2}+b x+c=0$

For equal roots $D=0$

$\Rightarrow \mathrm{b}^{2}=4 \mathrm{ac}$

Case I : $a c=1$

$(\mathrm{a}, \mathrm{b}, \mathrm{c})=(1,2,1)$

Case II : ac $=4$

$(a, b, c)=(1,4,4)$

or $(4,4,1)$

or $(2,4,2)$

Case III : ac =9

$(a, b, c)=(3,6,3)$

Required probability $=\frac{5}{216}$