JEE Mains · Maths · STD 12 - 13. probability
Let \(a, b, c \in \{1, 2, 3, 4\}\). If the probability, that \(ax^2 + 2\sqrt{2}\,bx + c > 0\) for all \(x \in \mathbb{R}\), is \(\dfrac{m}{n}\), \(\gcd(m, n) = 1\), then \(m + n\) is equal to _______.
- A 81
- B 82
- C 83
- D 84
Answer & Solution
Correct Answer
(A) 81
Step-by-step Solution
Detailed explanation
For the quadratic expression \(ax^2 + 2\sqrt{2}bx + c > 0\) for all \(x \in \mathbb{R}\), the leading coefficient must be positive and the discriminant must be negative. Since \(a \in \{1, 2, 3, 4\}\), the condition \(a > 0\) is always satisfied. The discriminant condition is:…
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