NTA Abhyas JEE Main2020MathematicsQuadratic EquationPractice

If - π < θ < π , the equation cos ⁡ 3 θ + 1 x 2 + 2 cos ⁡ 2 θ - 1 x + 1 - 2 cos ⁡ θ = 0 has more than two roots for

Options

Ano value of θ
Bone value of θ
Ctwo value of θ
Dall values of θ

Correct answer

A. no value of θ

Step-by-step solution

Given equation has more than two roots if it is an identity ⇒ cos ⁡ 3 θ + 1 = 0 ;  2 cos ⁡ 2 θ - 1 = 0  a n d  1 - 2 cos ⁡ θ = 0 ⇒ cos ⁡3 θ = - 1 ⇒ θ = ± π 3 which does not satisfy 2 cos ⁡ 2 θ - 1 = 0 Hence, no value possible

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