AP EAMCET · Maths · Probability
Let \(S\) be the set of all quadratic equations of the form \(x^2+b x+c=0\), where \(b, c \in\{1,2,3\), \(4,5,6\}\). If an equation is selected at random from \(S\), then the probability that the equation has real roots is
- A \(\frac{9}{12}\)
- B \(\frac{9}{36}\)
- C \(\frac{19}{36}\)
- D \(\frac{7}{36}\)
Answer & Solution
Correct Answer
(C) \(\frac{19}{36}\)
Step-by-step Solution
Detailed explanation
Given \(S=\left\{x^2+b x+c=0\right.\); \[ b, c \in\{1,2,3,4,5,6\}\} \] Since, we know that a quadratic equation \(a x^2+b x+c=0\) has real roots, if \(b^2-4 a c \geq 0\) \(\because a=1\), hence condition for the given equation is \[ b^2-4 c \geq 0 \] Total number of equations in…
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