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    Question

    In each question two equations numbered (I) and (II) are given. You should solve both the equations and mark appropriate answer.

    I. x2– 9x + 18 = 0

    II. y2– 5y + 6 = 0

    A if x > y Correct Answer Incorrect Answer
    B if x ≥ y Correct Answer Incorrect Answer
    C if x < y Correct Answer Incorrect Answer
    D if x ≤ y Correct Answer Incorrect Answer
    E if x = y or the relation between x and y cannot be established Correct Answer Incorrect Answer

    Solution

    I. x2 – 9x + 18 = 0
    => x2– 6x – 3x + 18 = 0
    => x (x – 6) – 3(x – 6) = 0
    => x = 6, 3
    II. y2 – 5y + 6 = 0
    => y2– 3y - 2y + 6 = 0
    => y (y – 3) - 2 (y – 3) = 0
    => y = 3, 2
    Hence, x ≥ y
    Alternate Method:
    if signs of quadratic equation is - ve and +ve then the roots of equation will be +ve and +ve.
    So, x = 6, 3
    y = 3, 2
    After comparing we can conclude that x ≥ y.

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