Quadratic EquationMedium
Question
If 1 lies between the roots of the quadratic equation 3x2 - 3sinθ.x + 2sin2θ = 2, then range of ′θ′ is (n ∈ I)
Options
A.(nπ, 2nπ)
B.
C.
D.
Solution
f(1) < 0 ⇒ 3 - 3sinθ - 2cos2θ < 0
2 sin2 θ - 3 sinθ + 1 < 0
⇒ (2 sinθ - 1) (sinθ - 1) < 0
< sin θ < 1
θ ∈
2 sin2 θ - 3 sinθ + 1 < 0
⇒ (2 sinθ - 1) (sinθ - 1) < 0
< sin θ < 1θ ∈
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