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Each of a and b can take values 1 or 2 with equal probability. The probability that the equation ax2 + bx + 1 = 0 has real roots, is equal to (A)1/2 (B)1/4 (C)1/8 (D)1/16

Each of a and b can take values 1 or 2 with equal probability. The probability that the equation ax2 + bx + 1 = 0 has real roots, is equal to


(A)1/2




(B)1/4




(C)1/8



(D)1/16

Grade:

2 Answers

Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
Dear student

for real root

a b root type

1 1 nr
1 2 nr
2 1 r
2 2 nr

Probability 1/4

Regards
Vikas TU
14149 Points
3 years ago
Since, b2 ≥ 4ac and since the maximum value of b2 is 36, ac=10,11,12,…,36 is not possible. So, the probability that the above equation has real root is 43/216 ∴ Required probability =1−43/216 = 173/216

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