Question
Question: The values of 'a' for which (a<sup>2</sup> – 1)x<sup>2</sup> + 2 (a – 1) x + 2 is positive for any x...
The values of 'a' for which (a2 – 1)x2 + 2 (a – 1) x + 2 is positive for any x is –
A
a ³ 1
B
a £ 1
C
a > – 3
D
a £ – 3 or a > 1
Answer
a £ – 3 or a > 1
Explanation
Solution
As f(x) > 0
\ a2 – 1 > 0 & D < 0
aĪ (–, –1) Č (1, ) {2 (a –1)}2 – 8(a2 –1) < 0
a2 + 1 – 2a – 2a2 + 2 < 0
– a2 – 2a + 3 < 0
a2 + 2a – 3 > 0
(a – 1) (a + 3) > 0
aĪ (– , – 3) Č (1, )
\ a £ – 3 or a > 1