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Question: Answered & Verified by Expert
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
MathematicsProbabilityAP EAMCETAP EAMCET 2009
Options:
  • A $\frac{1}{9}$
  • B $\frac{2}{9}$
  • C $\frac{3}{9}$
  • D $\frac{4}{9}$
Solution:
1713 Upvotes Verified Answer
The correct answer is: $\frac{4}{9}$
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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