Question

The set of values of k for which $x^2-kx+si{n}^{-1}\left(sin4\right)>0$ for all real x is

• A. ϕ
• B. (-2, 2)
• C. R
• D. (-2, -2)

Answer 1

The correct option is A

ϕ

$si{n}^{-1}\left(sin4\right)=si{n}^{-1}\left\{sin\right(\pi -4\left)\right\}=\pi -4$
$(\because -\frac{\pi }{2}<\pi -4<\frac{\pi }{2})$
$\because$ We have, $x^2-kx+\pi -4>0$ for all x $ϵ$ R
$\because D<0,ie,k^2-4(4-\pi )<0$, which is not true for any real k.