Find the set S that denotes the set of all values of 'α' for which the roots of the equation (1 - α)x2 - 6αx + 8α = 0 is greater than 2.
Explanation:
αf(x) = (1 - α)x2 - 6αx + 8α = 0
Now roots are greater than 2 therefore,
-b2a > 2
f(2) > 0
D > 0
-b2a > 0
2(1 - α) > 0
αα-1 < 0
α ∈ (0, 1)
(1 − α ) 4 − 12α + 8α > 0 4 − 8α > 0
a < 12
36α2 - 32α (1 - α) > 0
68α2 - 32α > 0
α(68α - 32) > 0
α ∈ (-∞, 0) ∪ 3268,∞
Taking the intersection of all we get α ∈ 3268,12
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.