The coefficients a , b and c of the quadratic equation, a x 2 + b x + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is:

Step-by-step solution

a x 2 + b x + c = 0 a ,   b ,   c ∈ 1 ,   2 ,   3 ,   4 ,   5 ,   6 n ( s ) = 6 × 6 × 6 = 216 For equal root D = 0 ⇒ b 2 = 4 a c Case I: a c = 1 a , b , c = 1 , 2 , 1 Case II: a c = 4 a , b , c = 1 , 4 , 4 or 4 , 4 , 1 or 2 , 4 , 2 Case-III: a c = 9 a , b , c = 3 , 6 , 3 Required probability = 5 216