3
advanced-math

Solve: x25x+60x^2 - 5x + 6 \leq 0

A

2x32 \leq x \leq 3

B

x2x \leq 2 or x3x \geq 3

C

2<x<32 < x < 3

D

x3x \leq 3

Correct Answer: A

Choice A is the correct answer.

  1. Factor: (x2)(x3)0(x - 2)(x - 3) \leq 0.
  2. Roots: 2 and 3.
  3. Parabola opens upward, so it is negative between the roots.
  4. Solution: 2x32 \leq x \leq 3.

Choice B is incorrect. Choice C is incorrect because it excludes endpoints. Choice D is incorrect.