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    Question

    For which values of x is the expression 25x - 5x² - 100

    positive?
    A 1 > x > 4 Correct Answer Incorrect Answer
    B 1 < x < 4 Correct Answer Incorrect Answer
    C 1 ≤ x ≤ 4 Correct Answer Incorrect Answer
    D 1 ≥ x ≥ 4 Correct Answer Incorrect Answer

    Solution

    ATQ,

    So, 25x - 5x² - 100 > 0

    Or, 5x² - 25x + 100 < 0

    Or, 5x² - 20x - 5x + 100 < 0

    Or, 5x(x - 4) -5(x - 4) < 0

    Or, (5x - 5)(x - 4) < 0

    So, x = 1 and x = 4

    Hence, the expression is positive between 1 and 4.

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