Solve the inequality x^2 - 7x + 10 > 0. Which of the following is the solution set?
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Correct answer
A. (-∞, 2) ∪ (5, ∞)
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 union of intervals where the quadratic is positive.
Why this answer is correct
Factor x^2 - 7x + 10 = (x - 2)(x - 5). The roots are 2 and 5. The parabola opens upward, so the expression is positive when x < 2 or x > 5. Thus the solution is (-∞, 2) ∪ (5, ∞).
Example
For x^2 - 3x + 2 > 0, factor as (x-1)(x-2)>0; solution (-∞,1) ∪ (2,∞).
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