5
advanced-math

Solve: x24x+30x^2 - 4x + 3 \leq 0

A

1x31 \leq x \leq 3

B

x1x \leq 1 or x3x \geq 3

C

1<x<31 < x < 3

D

x3x \leq 3

Correct Answer: A

Choice A is the correct answer.

  1. Factor: (x1)(x3)0(x - 1)(x - 3) \leq 0.
  2. Roots: 1 and 3.
  3. Test: Between 1 and 3 (e.g., x=2x=2), (21)(23)=1(1)=1(2-1)(2-3) = 1(-1) = -1 (Negative).
  4. Conclusion: The expression is 0\leq 0 between the roots, inclusive.

Choice B is incorrect because that is for 0\geq 0. Choice C is incorrect because it excludes the endpoints. Choice D is incorrect.