Question
Question: f(x) = \(\frac{(2a - 1)x^{2} + 2(a + 1)x + (2a - 1)}{x^{2} - 2x + 40}\) is always negative is...
f(x) = x2−2x+40(2a−1)x2+2(a+1)x+(2a−1) is always negative is
A
(–∞, 0)
B
(0, ∞)
C
(–∞, 1/2)
D
None
Answer
(–∞, 0)
Explanation
Solution
Q (2a –1)x2 +2(a+1)x +(2a –1) < 0 ∀ x ∈ R
∴ 2a – 1 < 0
a <21 … (i)
Now D < 0
4(a + 1)2 – 4(2a –1)2 < 0
a (a – 2) > 0
a < 0, a > 2 … (2)
from (1) and (2), a < 0