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JEE Main20203 Sep 2020Evening ShiftMathematicsQuadratic EquationActual

The set of all real values of λ for which the quadratic equation λ 2 + 1 x 2 - 4 λ x + 2 = 0 always have exactly one root in the interval ( 0 , 1 ) is :

Options

  1. A− 3 ,   − 1
  2. B0 ,   2
  3. C( 1 ,   3 ]
  4. D( 2 ,   4 ]

Correct answer

C. ( 1 ,   3 ]

Step-by-step solution

f 0 · f 1 ≤ 0 ⇒ 2 λ 2 + 1 - 4 λ + 2 ≤ 0 ⇒ 2 λ 2 - 4 λ + 3 ≤ 0 ⇒ λ - 1 λ - 3 ≤ 0 ⇒ λ ∈ 1 ,   3 But at λ = 1 , both roots are 1 . So, λ ≠ 1

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