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    Question

    A set of 2 equations is given below. Read the information carefully and answer the question based on it Equation (I): x² - px + q = 0 has roots 'm' and 5. Equation (II): x² - (p - 2)x + (q - 6) = 0 has roots 'm' and 3.

    Another equation (III) x² - 8x + 15 = 0 is given. Which of the following is/are correct about it?

    1.      Roots of equation (III) are less than that of equation (II).

    2.      Equation (III) has one root equal to the value of 'm'.

    3.      Equation (III) has roots greater than (q - p).

    A Only 1 and 3 Correct Answer Incorrect Answer
    B Only 1 and 2 Correct Answer Incorrect Answer
    C Only 2 Correct Answer Incorrect Answer
    D None of the above Correct Answer Incorrect Answer
    E All of the above Correct Answer Incorrect Answer

    Solution

    Equation (III): x² - 8x + 15 = 0 can be factored as (x - 3)(x - 5) = 0 Roots of Equation (III) are 3 and 5. From Equation (II), m = 3. q - p = 15 – 8 = 7 Answer: (c) Only 2

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