Ques. 1JEE Main 2024, 5 April (Morning Shift)
The coefficients a, b, c in the quadratic equation ax2 + bx + c = 0 are chosen from the set \1, 2, 3, 4, 5, 6, 7, 8\. The probability of this equation having repeated roots is :
- 1128
- 164
- 3256
- 3128
Answer
(2) 164
Solution
Total cases = 83 = 512
Repeated roots ⇒ b2 = 4ac ⇒ b even, ac = b24
b = 2: ac = 1 → (1, 1) ⇒ 1 way
b = 4: ac = 4 → (1, 4), (2, 2), (4, 1) ⇒ 3 ways
b = 6: ac = 9 → (3, 3) ⇒ 1 way
b = 8: ac = 16 → (2, 8), (4, 4), (8, 2) ⇒ 3 ways
P = 8512 = 164
Answer: (2)