JEE Mains · Maths · STD 12 - 13. probability
The coefficients \(a, b, c\) in the quadratic equation \(a x^2+b x+c=0\) are from the set \(\{1,2,3,4,5,6\}\). If the probability of this equation having one real root bigger than the other is \(p\), then \(216\) p equals:
- A \(57\)
- B \(38\)
- C \(19\)
- D \(76\)
Answer & Solution
Correct Answer
(B) \(38\)
Step-by-step Solution
Detailed explanation
\( \mathrm{D}>0 \) \( \mathrm{~b}^2>4 \mathrm{ac} \) \( \mathrm{b}=3:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1) \) \( \mathrm{b}=4:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1) \) \( \mathrm{b}=5:(\mathrm{a}, \mathrm{c})=(1,1)(1,2)(2,1)(1,3)(3,1)(1,4)(4,1) \)…
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