Probability

The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are from the set \1, 2, 3, 4, 5, 6\. If the probability of this equation having one real root bigger than the other is p, then 216p equals :

1. 38
2. 76
3. 57
4. 19

Answer

(1) 38

Solution

One real root bigger than the other real and distinct roots b2 > 4ac; total cases = 63 = 216

b = 1, 2: ac < 1 0 cases

b = 3: ac 2: (1, 1), (1, 2), (2, 1) 3

b = 4: ac 3: above + (1, 3), (3, 1) 5

b = 5: ac 6: ac = 1, 2, 3, 4, 5, 6 give 1 + 2 + 2 + 3 + 2 + 4 = 14

b = 6: ac 8: 14 + (2, 4), (4, 2) 16

Favourable = 3 + 5 + 14 + 16 = 38 p = 38216 216p = 38

Answer: (1)