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    Two quadratic equations, x² - 5x + 6 = 0 and 2x² - kx + 6 = 0, have one common root. What is the possible value of k?
    Question

    Two quadratic equations, x² - 5x + 6 = 0 and 2x² - kx + 6 = 0, have one common root. What is the possible value of k?

    A.

    5

    B.

    11

    C.

    7

    D.

    9

    Correct option is C

    Given:

    Two equations:

    x25x+6=0x^2 - 5x + 6 = 0​​

    2x2kx+6=02x^2 - kx + 6 = 0​​

    They have one common root.

    Concept Used:

    If two quadratic equations share one root, then that root satisfies both equations.

    Solution:

    x25x+6=0x^2 - 5x + 6 = 0​​

    (x - 2)(x - 3) = 0

    x = 2, 3

    For common root 2:

    Substituting in second equation:

    (2)2 - 2k + 6 = 0

    8 - 2k + 6 = 0

    14 - 2k = 0

    k = 7

    For  common root = 3:

    (3)2 - 3k + 6 = 0

    18 - 3k + 6 = 0

    24 - 3k = 0

    k = 8

    Thus, Possible values of k: 7 or 8 

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