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Reviewed CSCA Mathematics question · Hard

Solve the inequality 3x^2 - 10x + 3 < 0. Which of the following is the solution set?

  1. (-∞, 1/3) ∪ (3, ∞)
  2. (-1/3, 3)
  3. (1/3, 3)
  4. (-∞, -3) ∪ (-1/3, ∞)
Show the answer and explanation

Correct answer

C. (1/3, 3)

Principle or equation

For a quadratic inequality ax^2 + bx + c < 0 with a > 0, find the roots and test intervals; the solution is the interval between the roots if the parabola opens upward.

Why this answer is correct

Factor the quadratic: 3x^2 - 10x + 3 = (3x - 1)(x - 3). The roots are x = 1/3 and x = 3. Since the coefficient of x^2 is positive, the parabola opens upward, so the expression is negative between the roots. Thus the solution is (1/3, 3).

Example

Solve x^2 - 5x + 6 < 0. Factor to (x - 2)(x - 3) < 0, so the solution is (2, 3).

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