Question

The coefficients a, b and c of the quadratic equation, ax² + bx + c = 0 are obtained by throwing a dice three times. The probability that this equation has equal roots is:

(1) 1/72

(2) 5/216

(3) 1/36

(4) 1/54

Answer 1

Correct option is (2) 5/216

ax² + bx + c = 0 

For equal roots D = 0 

⇒ b² = 4ac 

Case I : ac = 1

(a, b, 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 = 5/216