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      Question

      Find the interval of x where the expression 21x - 3x² - 54

      is greater than zero.
      A 1 > x > 6 Correct Answer Incorrect Answer
      B 1 < x < 6 Correct Answer Incorrect Answer
      C 1 ≤ x ≤ 6 Correct Answer Incorrect Answer
      D 1 ≥ x ≥ 6 Correct Answer Incorrect Answer

      Solution

      ATQ,

      So, 21x - 3x² - 54 > 0

      Or, 3x² - 21x + 54 < 0

      Or, 3x² - 18x - 3x + 54 < 0

      Or, 3x(x - 6) -3(x - 6) < 0

      Or, (3x - 3)(x - 6) < 0

      So, x = 1 and x = 6

      Therefore, the expression is positive between 1 and 6.

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