5

Set 17: Quadratic Equations

Explanation

Answer: A

Solve: x(x+4)0x(x + 4) \geq 0

A.

x0x \geq 0 or x4x \leq -4

✓ Correct
B.

4x0-4 \leq x \leq 0

C.

x0x \geq 0

D.

x4x \leq -4

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Roots: x=0x = 0 and x=4x = -4. 2. Region: Since it opens upward and we want 0\geq 0, we look for the outside tails. 3. Order: 4-4 is less than 00. 4. Solution: Left of smaller root (x4x \leq -4) or right of larger root (x0x \geq 0). Choice B is incorrect because that is where it is negative. Choice C is incorrect because it misses the left part. Choice D is incorrect because it misses the right part.

Key Steps:

The correct answer is x0x \geq 0 or x4x \leq -4

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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