Question

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

• A. (-4, 4)
• B. $(\infty ,-4)\cup (4,\infty )$
• C. $\varphi$
• D. None of these

Answer 1

The correct option is C $\varphi$

$x^2-px+si{n}^{-1}\left(sin4\right)>0$ for all real x.
$\Rightarrow x^2-px+si{n}^{-1}sin(\pi -4)>0$
$\Rightarrow x^2-px+(\pi -4)>0\forall x\in R$
$\Rightarrow D=p^2-4(\pi -4)<0$
$\Rightarrow p^2+16-4\pi <0$
Since $16-4\pi >0,p^2+16-4\pi$ can not be negative for any value of $p\in R$.
$\therefore$ Set of values of $p=\varphi$.