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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 – 18x + 81 = 0 II.

    y2 – 3y - 28 = 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 – 18x + 81 = 0 => x2 – 9x – 9x + 81 = 0 => x (x – 9) – 9(x – 9) = 0 => x = 9, 9 II. y2 – 3y - 28 = 0 => y2 – 7y + 4y - 28 = 0 => y (y – 7) + 4 (y – 7) = 0 => y = 7, -4 Hence, x > y Alternate Method: if signs of quadratic equation is - ve and +ve respectively then the roots of equation will be +ve and +ve. So, roots of first equation = x = 9, 9 if signs of quadratic equation is - ve and -ve then the roots of equation will be +ve and -ve respectively. (note: +ve sign will come in larger value) So, roots of second equation = x = 7, -4 After comparing we can conclude that x > y.

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