Solve the inequality x^2 - 5x + 6 < 0.
Show the answer and explanation
Correct answer
B. 2 < x < 3
Principle or equation
For a quadratic inequality ax^2 + bx + c < 0, factor the quadratic, find the roots, and test intervals on the number line. The solution is the interval(s) where the quadratic is negative.
Why this answer is correct
Factor: x^2 - 5x + 6 = (x - 2)(x - 3). Roots are x = 2 and x = 3. Test intervals: For x < 2, both factors negative, product positive. For 2 < x < 3, first positive, second negative, product negative. For x > 3, both positive, product positive. Thus the inequality holds for 2 < x < 3.
Example
Solve x^2 - 4 < 0: (x-2)(x+2)<0, roots -2 and 2, solution -2 < x < 2.
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