LimitsHard
Question
Let α, β be the roots of equation ax2 + bx + c = 0, where 1 < α < β and 
= 1, then which of the following statements is incorrect
= 1, then which of the following statements is incorrectOptions
A.a > 0 and x0 < 1
B.a > 0 and x0 > β
C.a < 0 and α < x0 < β
D.a < 0 and x0 < 1
Solution
α, β be the roots of the equation ax2 + bx + c = 0
where 1 < α < β.
(i) if a > 0
So ax2 + bx + c > 0 when x ∈ (-∞, α) ∪ (β, ∞)
So
when a > 0 and x ∈ (-∞, α) ∪ (β, α)
(ii) If a < 0
So ax2 + bx + c > 0 when x ∈ (α, β)
when a < 0 and x ∈ (α, β)
So (A) a > 0 and x0 < 1 right
(B) a > 0 and x0 > β right
(C) a < 0 and a < x0 < β right
(D) a < 0 and x0 < 1 wrong
where 1 < α < β.
(i) if a > 0
So ax2 + bx + c > 0 when x ∈ (-∞, α) ∪ (β, ∞)
So
when a > 0 and x ∈ (-∞, α) ∪ (β, α)
(ii) If a < 0
So ax2 + bx + c > 0 when x ∈ (α, β)
when a < 0 and x ∈ (α, β)
So (A) a > 0 and x0 < 1 right
(B) a > 0 and x0 > β right
(C) a < 0 and a < x0 < β right
(D) a < 0 and x0 < 1 wrong
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