If p , q are chosen randomly with replacement from the set { 1 , 2 , 3 , …… 10 } , the probability, that the roots of the equation x 2 + p x + q = 0 are real, is 50 k 2 + 6 then k =

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MathematicsProbabilityGeneral (Event SS, Definitions, Odd against/Favour)Medium2 minQB

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If $p, q$ are chosen randomly with replacement from the set ${1, 2, 3, \dots\dots 10}$ , the probability, that the roots of the equation $x^{2} + p x + q = 0$ are real, is $\frac{k ^{2} + 6}{50}$ then $k =$

Answer:

Solution:

$p^{2} \geq 4 q \Rightarrow$

The total number of pairs $(p, q)$ is $1 + 2 + 4 + 6 + 9 + 40 = 62$

$Probability = \frac{62}{10.10} = \frac{31}{50}$

Stream:JEESubject:MathematicsTopic:ProbabilitySubtopic:General (Event SS, Definitions, Odd against/Favour)

⏱ 2mℹ️ Source: QB

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