COMEDK · Maths · 36. Probability
The probability of choosing randomly a number \(c\) from the set \(\{1,2,3, \ldots 9\}\) such that the quadratic equation \(x^2+4 x+c=0\) has real roots, is
- A \(\dfrac{1}{9}\)
- B \(\dfrac{2}{9}\)
- C \(\dfrac{3}{9}\)
- D \(\dfrac{4}{9}\)
Answer & Solution
Correct Answer
(D) \(\dfrac{4}{9}\)
Step-by-step Solution
Detailed explanation
The quadratic equation \(x^2 + 4x + c = 0\) has real roots if and only if its discriminant \(D \ge 0\). The discriminant \(D\) is given by \(D = b^2 - 4ac\). Here \(a = 1\), \(b = 4\), and \(c = c\). Substituting the values, \(D = 4^2 - 4(1)(c) = 16 - 4c\). For real roots,…
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