Solve the inequality x^2 - 5x + 6 < 0. Which of the following is the solution set?
Show the answer and explanation
Correct answer
B. (2, 3)
Principle or equation
For a quadratic inequality ax^2 + bx + c < 0, factor the quadratic and determine the sign of the product on intervals defined by its roots.
Why this answer is correct
Factor x^2 - 5x + 6 = (x - 2)(x - 3). The roots are 2 and 3. Test intervals: (-∞, 2): product positive; (2, 3): product negative; (3, ∞): product positive. Since the inequality is < 0, the solution is (2, 3).
Example
Solve x^2 - x - 2 < 0: factor (x - 2)(x + 1) < 0, roots -1 and 2, solution (-1, 2).
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