The set $\left\{x \in \mathbb{R}: 4+11 x-3 x^2>0\right\}$ is the interval

• Correct answer
  A

  $\left(-\frac{1}{3}, 4\right)$
• B

  $(-, 4)$
• C

  $\left(-4, \frac{1}{3}\right)$
• D

  $\left(-4, \frac{-1}{3}\right)$

Solution

$\begin{aligned} & \text {Given: }\left\{x \in R: 4+11 x-3 x^2>0\right\} \\ & \because 4+11 x-3 x^2>0 \\ & \Rightarrow-(x-4)(3 x-1)>0 \\ & \Rightarrow(x-4)(3 x-1) < 0\end{aligned}$
$\therefore x \in\left(-\frac{1}{3}, 4\right)$

Hence, the correct answer is option: 'A'.