The set of all the possible real values of $a$ such that the inequality $\left(x-\left(a-1\right)\right)\left(x-\left(a^2+2\right)\right)<0$ holds for all $x\in \left(-1,3\right)$, is

• A

  $\left(1,\infty \right)$
• Correct answer
  B

  $\left(-\infty ,-1\right)$
• C

  $\left(-\infty ,1\right)$
• D

  $\left(0,1\right)$

Solution

$a-1<-1$ and $a^2+2>3$
$a<0$ and $a^2>1$
$a<0$ and $a>1$ or $a<-1$
$\Rightarrow a<-1$

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