The coefficients a ,   b and c of the quadratic equation, a x 2 + b x + c = 0 are obtained by throwing…

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

$a, b, c\in \{1, 2, 3, 4, 5, 6\}$

$n\left(s\right)=6\times 6\times 6=216$

For equal root $D=0$

$\Rightarrow b^2=4ac$

Case I: $ac=1$

$\left(a,b,c\right)=\left(1,2,1\right)$

Case II: $ac=4$

$\left(a,b,c\right)=\left(1,4,4\right)$

or $\left(4,4,1\right)$

or $\left(2,4,2\right)$

Case-III: $ac=9$

$\left(a,b,c\right)=\left(3,6,3\right)$

Required probability $=\frac{5}{216}$