Question

If for real values of x. x2 – 3x + 2 > 0 and
x2 – 3x - 4 3 0, then-
(A) -1 <x< 1
(B) -1 <x<4
(C)-1 <x< 1 and 2 XS4
(D) 2<X < 4​

Answer 1

Hey Pretty Stranger!

→ x² - 3x + 2 > 0

→ x² - 2x - x + 2 > 0

→ x( x - 2) + 1( x - 2) > 0

→ (x - 1) (x - 2) > 0

$\therefore$ x ∈ ( -1 , ∞) ∪ (2 , ∞)... i)

→ x² - 3x - 4 < 0

→ x² - 4x + x - 4 < 0

→ x( x - 4) + 1(x - 4) < 0

→ (x + 1) (x - 4) < 0

$\therefore$ x ∈ [-1 , 4]... ii)

From eq i) and ii)

x ∈ [ -1 , 1 ] ∪ [ 2, 4 ]

Option c) -1 ≤ x < 1 or 2 < x ≤ 4 is the required answer.