Question:
If \( l, m \) represent any two elements (identical or different) of the set \( \{1, 2, 3, 4, 5, 6, 7\} \), then the probability that \( lx^2 + mx + 1>0 \,\, \forall x \in \mathbb{R} \) is
If \( l, m \) represent any two elements (identical or different) of the set \( \{1, 2, 3, 4, 5, 6, 7\} \), then the probability that \( lx^2 + mx + 1>0 \,\, \forall x \in \mathbb{R} \) is
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For a quadratic to be positive for all real \( x \), ensure the leading coefficient is positive and the discriminant is negative.
Updated On: Jun 4, 2025
- \( \dfrac{12}{\binom{7}{2}} \)
- \( \dfrac{22}{72} \)
- \( \dfrac{10}{\binom{7}{2}} \)
- \( \dfrac{36}{72} \)
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The Correct Option is B
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