Straight LineHard
Question
Consider the family of lines x(a + b) + y = 1, where a, b and c are the roots of the equation x3 - 3x2 + x + λ = 0 such that c ∈ [1,2]. If the given family of lines makes triangle of area ′A′ with coordinate axis, then maximum value of ′A′ (in sq. units) will be -
Options
A.1/4
B.1
C.1/8
D.1/2
Solution
Since a, b, c are the roots of the equation
x3 - 3x2 + x + λ = 0
⇒ a + b + c = 3 ⇒ a + b = 3 - c
Now area of the triangle will be
A =
⇒
As A is an increasing function & c ∈ [1,2]
∴ Amax =
sq. units.
x3 - 3x2 + x + λ = 0
⇒ a + b + c = 3 ⇒ a + b = 3 - c
Now area of the triangle will be
A =
⇒
As A is an increasing function & c ∈ [1,2]
∴ Amax =
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