TS EAMCET · Maths · 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 \(\frac{1}{9}\)
- B \(\frac{2}{9}\)
- C \(\frac{3}{9}\)
- D \(\frac{4}{9}\)
Answer & Solution
Correct Answer
(D) \(\frac{4}{9}\)
Step-by-step Solution
Detailed explanation
Given, \(x^2+4 x+c=0\) For real roots, \(\begin{aligned} D & =b^2-4 a c \geq 0 \\ & =16-4 c \geq 0 \end{aligned}\) \(\Rightarrow \quad c=1,2,3,4\) will satisfy the above inequality. \(\therefore\) Required probability \(=\frac{4}{9}\)
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