Question

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

• A. $\left(1 , \infty\right)$
• B. $\left(- \infty , - 1\right)$
• C. $\left(- \infty , 1\right)$
• D. $\left(0 , 1\right)$

Answer 1

Answer: (B)

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