Solve the equation: $x^2 - 5x + 6 \geq 0 $.
- $ x \in (- \infty , 2] \cup [3, \infty)$
- $ x \in [2,3] $
- $ x \in (- \infty , -1] \cup [6, \infty)$
- $ x \in [-1,6] $
Reveal answer
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A
Correct answer
Explanation
x^2 - 5x + 6 >= 0 factors to (x-2)(x-3) >= 0. The inequality holds when x <= 2 or x >= 3.
AI explanation
Factoring the quadratic inequality x^2 - 5x + 6 >= 0 gives (x - 2)(x - 3) >= 0. The critical values are x = 2 and x = 3, which divide the number line into intervals. Testing the intervals shows the expression is non-negative when x is less than or equal to 2, or greater than or equal to 3, making the solution set x in (-infinity, 2] union [3, infinity).