9

Set 1: Quadratic Equations (Intermediate)

Explanation

Answer: A

Solve: (x2)(x5)>0(x - 2)(x - 5) > 0

A.

x<2x < 2 or x>5x > 5

✓ Correct
B.

2<x<52 < x < 5

C.

x>5x > 5

D.

x<2x < 2

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Roots: x=2x = 2 and x=5x = 5. 2. Direction: The leading term is x2x^2 (positive), so it opens upward. 3. Inequality: We want >0> 0 (above the axis). 4. Region: For an upward parabola, positive values are on the "outside" tails. 5. Solution: x<2x < 2 or x>5x > 5. Choice B is incorrect because that is where it is negative (between roots). Choice C is incorrect because it misses the left tail. Choice D is incorrect because it misses the right tail.

Key Steps:

The correct answer is x<2x < 2 or x>5x > 5

Why others are wrong:
B: Choice B is incorrect and may result from a calculation error.
C: Choice C is incorrect and may result from a calculation error.
D: Choice D is incorrect and may result from a calculation error.

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