The set of all the possible real values of a such that the inequality (x-(a-1))(x-(a2+2))

Question

The set of all the possible real values of a such that the inequality (x-(a-1))(x-(a2+2))<0 holds for all x ∈(-1,3) , is (A) (1 , ∞) (B) (- ∞ , - 1) (C) (- ∞ , 1) (D) (0 , 1)

Tardigrade Admin · Accepted Answer

a-1 < -1 and a2+2>3 a < 0 and a2>1 a < 0 and a>1 or a < -1 ⇒ a < -1

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

$(1, \infty)$

$(- \infty, - 1)$

$(- \infty, 1)$

$(0, 1)$

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

Q. The set of all the possible real values of a such that the inequality (x−(a−1))(x−(a2+2))<0 holds for all x∈(−1,3) , is

(1,∞)

(−∞,−1)

(−∞,1)

(0,1)