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The set of all the values of ‘a’ for which the roots of the equation (a-2)x² - 2ax + a = 0 lies in the interval (-2, 1).

Option 1 -

a ∈ [0, 8/9) U {2}

Option 2 -

a ∈ (0, 8/9) U {2}

Option 3 -

a ∈ (0, 8/9)

Option 4 -

29/3


0 6 Views | Posted 3 weeks ago
Asked by Shiksha User

  • 1 Answer

  • R

    Answered by

    Raj Pandey | Contributor-Level 9

    3 weeks ago
    Correct Option - 1


    Detailed Solution:

    Case-I : a - 2 > 0

    F ( - 2 ) > 0

    4 ( a - 2 ) + 4 a + a > 0

    9 a - 8 > 0

    a > 8 9

    F ( 1 ) > 0

    a - 2 - 2 a + a > 0

      - 2 > 0  (not possible)

    Case-II : a - 2 < 0 ; a < 2

    F ( - 2 ) < 0 ⇒ a < 8 9

    F ( 1 ) < 0 ⇒ a ∈ R

    - 2 < - b 2 a < 1 a < 4 3 a ∈ 0 , 8 9 ∪ { 2 }

    D ≥ 0 a ≥ 0

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