Each coefficient in the equation `ax^(2)+bx+c=0` is obtained by rolling a die. Find the probability that the equation has equal roots.

Explanation

The three coefficient a,b and c are determined by rolling a die three times.
Each die has six possibilities.
`:.` the sample space has `6xx6xx6=216` points.
`:.n(S)=216`
Let A be the event that the equation has equal roots.
Then the discriminant `(Delta)=b^(2)-4ac=0`.

`A={(2,1,1),(4,1,4),(4,4,1),(4,2,2),(6,3,3)}`
`:n(A)=5`
`:.P(A)=(n(A))/(n(S)):.P(A)=5/216`
Ans. The probability that the equation `ax^(2)+bx+c=0` has equal roots is `5/216`.