Q78 / 160 · TS EAMCET 2009 · Mathematics
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$\frac{3}{9}$
- Correct answerD$\frac{4}{9}$
Solution
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 $=\frac{4}{9}$
Hence, the correct answer is option: 'D'.