3

Set 6: Quadratic Equations (Advanced)

Explanation

Answer: A

Solve: x2−4x+3≤0x^2 - 4x + 3 \leq 0

A.

1≤x≤31 \leq x \leq 3

✓ Correct
B.

x≤1x \leq 1 or x≥3x \geq 3

C.

1<x<31 < x < 3

D.

x≤3x \leq 3

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Factor: (x−1)(x−3)≤0(x - 1)(x - 3) \leq 0. 2. Roots: 1 and 3. 3. Test: Between 1 and 3 (e.g., x=2x=2), (2−1)(2−3)=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.

Key Steps:

•

The correct answer is 1≤x≤31\leq x \leq 3

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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