The value of k so that the equation  x3−12x+k=0 has distinct roots in [0, 2] is

The value of k so that the equation  x312x+k=0 has distinct roots in [0, 2] is

  1. A

    4

  2. B

    2

  3. C

    -2

  4. D

    none of these

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    Solution:

    If α and β are real and distinct roots of x312x+k=0. Then f(x)=x312x+k satisfies 

    f(α)=f(β)=0 then there  γ[α,β][0,2] such that

    f(γ)=0i.e.,  3v212=0γ=±2. Not possible.

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