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    Question

    In the following question two equations are given in variables x and y. You have to solve these equations and determine the relation between x and y.

    I. 6x2 + 19x + 10 = 0 II.

    y2 + 10y + 25 = 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 x = y or relation cannot be established between x and y Correct Answer Incorrect Answer

    Solution

    I. 6x2 + 19x + 10 = 0 => 6x2 + 15x + 4x + 10 = 0 =>3x(2x + 5) + 2(2x + 5) = 0 => (2x + 5) (3x + 2) = 0 => x = -5/2, -2/3 II. y2 + 10y + 25 = 0 =>y2 + 5y + 5y + 25 = 0 => y(y + 5) + 5(y + 5) = 0 => (y + 5) (y + 5) = 0 => y = -5, -5 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 = -5/2, -2/3 So, roots of second equation = y = -5, -5 After comparing we can conclude that x > y.

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