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