Question
Question: The range of a for which the equation x<sup>2</sup> + ax – 4 = 0 has its smaller root in the interva...
The range of a for which the equation x2 + ax – 4 = 0 has its smaller root in the interval (–1, 2) is
A
(–∞, –3)
B
(0, 3)
C
(0, ∞)
D
(–∞, –3) ∪ (0, ∞)
Answer
(–∞, –3)
Explanation
Solution
Clearly f(– 1) > 0, f(2) < 0
since f(0) = – 4 < 0
⇒ 1 – a – 4 > 0 ⇒ – a – 3 > 0 ⇒ – a > 3
or a < – 3 and 4 + 2a – 4 < 0
⇒ a < 0
⇒ a ∈ (– ∞, – 3).
