Which of the following values of x will satisfy the equation x2 – 7x + 12 < 0?
Which of the following values of x will satisfy the equation x2 – 7x + 12 < 0? Correct Answer 3 < x < 4
Calclation:
x2 – 7x + 12 < 0
⇒ x2 – 3x – 4x + 12 < 0
⇒ x(x – 3) – 4(x – 3) < 0
⇒ (x – 3) (x – 4) < 0
Case:1 (x – 3) > 0
⇒ x > 3 or (3, ∞)
Case:2 (x – 4) < 0
⇒ x < 4 or x ∈ (-∞, 4)
Taking union of both case, we get
x ∈ (-∞, 4) ∪ (3, ∞)
∴ 3 < x < 4
