Question

The largest integral value of $p$ for which graph of the function $f(x)=2 p^2-3 p \tan x+\tan ^2 x+1$ does not lie below $x$-axis for all $x \in\left(\frac{-\pi}{2}, \frac{\pi}{2}\right)$ is

• A. 0
• B. 2
• C. 3
• D. 8

Answer 1

Answer: (B)

$\text { Put } \tan x=t $
$y=t^2-3 p t+2 p^2+1, t \in R $
$D \leq 0 $
$9 p^2-4\left(2 p^2+1\right) \leq 0 \Rightarrow p^2-4 \leq 0 \Rightarrow p \in[-2,2]$
Hence largest integral value is 2