2
advanced-math

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

A

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

B

2<x<52 < x < 5

C

x>5x > 5

D

x<2x < 2

Correct Answer: A

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.