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    Question

    In the following questions, two equations I and II are given. You have to solve both equations and give answer as,

    I. x2 + 12√2 x + 22 = 0

    II. y2 - 13√2 y – 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 cannot be established. Correct Answer Incorrect Answer

    Solution

    I. x2 + 12√2 x + 22 = 0 (x + 11√2) (x + √2) = 0 x = - 11√2, -√2  II. y2 - 13√2 y – 28 = 0 (y - 14√2) (y + √2) = 0 y = - √2, 14√2 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 = -11√2, -√2 if signs of quadratic equation is -ve and -ve respectively then the roots of equation will be +ve and -ve. (note: -ve sign will come in smaller root) So, roots of second equation = y = - √2, 14√2 After comparing roots of quadratic equation we can conclude that x ≤ y.

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