Question
Question: If for real values of x, x<sup>2</sup> – 3x +2 \> 0 and x<sup>2</sup> – 3x – 4 ≤ 0, then...
If for real values of x, x2 – 3x +2 > 0 and x2 – 3x – 4 ≤ 0, then
A
–1 ≤ x < 1
B
– 1 ≤ x < 4
C
– 1 ≤ x < 1 & 2 < x ≤ 4
D
2 < x ≤ 4
Answer
– 1 ≤ x < 1 & 2 < x ≤ 4
Explanation
Solution
x2 – 3x + 2 > 0
x2 – 3x – 4 ≤ 0 (x – 1) (x – 2) > 0 (x – 4) (x + 1) ≤ 0
x ∈ (– ∞, 1) ∪ (2, ∞) x ∈ [–1, 4]
so x ∈ [–1, 1) ∪ (2, 4]