Question

If ${\sin }^{-1}\left(x^2-7x+12\right)=n\pi ,\forall n\in I$, then $x=$

• A. $-2$
• B. 4
• C. -3
• D. 5

Answer 1

Answer: (B)

${\sin }^{-1}\left(x^2-7x+12\right)=n\pi$
$\Rightarrow x^2-7x+12=\sin n\pi$
$\Rightarrow x^2-7x+12=0$$(\because \sin n\pi =0\forall n\in I)$
$\Rightarrow (x-4)(x-3)=0$
$\Rightarrow x=4,3$