AP EAMCET · Maths · Quadratic Equation
If \(l, m\) represent any two elements (identical or different) of the set \(\{1,2,3,4,5\), \(6,7\}\), then the probability that \(l x^2+m x+1>0 \forall x \in R\) is
- A \(\frac{12}{7 C_2}\)
- B \(\frac{22}{7^2}\)
- C \(\frac{10}{7 C_2}\)
- D \(\frac{36}{72}\)
Answer & Solution
Correct Answer
(B) \(\frac{22}{7^2}\)
Step-by-step Solution
Detailed explanation
\(l x^2+m x+1>0 \forall x \in R \implies l>0 \text{ and } m^2-4lGiven \(l,m \in \{1,2,3,4,5,6,7\}\), \(l>0\) is always true. Total pairs \((l,m) = 7 \times 7 = 49\). Favorable pairs for \(m^2 \(l=1: m^2\(l=2: m^2\(l=3: m^2\(l=4: m^2\(l=5: m^2\(l=6: m^2…
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