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      Question

      Between what values of x is the expression 18x - 3x² - 45

      positive?
      A 1 > x > 5 Correct Answer Incorrect Answer
      B 1 < x < 5 Correct Answer Incorrect Answer
      C 1 ≤ x ≤ 5 Correct Answer Incorrect Answer
      D 1 ≥ x ≥ 5 Correct Answer Incorrect Answer

      Solution

      ATQ,

      So, 18x - 3x² - 45 > 0

      Or, 3x² - 18x + 45 < 0

      Or, 3x² - 15x - 3x + 45 < 0

      Or, 3x(x - 5) -3(x - 5) < 0

      Or, (3x - 3)(x - 5) < 0

      So, x = 1 or x = 5

      For any value of 'x' > 5, the expression becomes positive.

      So, 'x' lies between 1 and 5.

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