Set 3: Quadratic Equations

Explanation

Answer: A

Solve: $3(x - 2)^2 = 12$

$x = 4, 0$

✓ Correct

$x = 6, -2$

$x = 4, -4$

$x = 2 \pm \sqrt{12}$

Detailed Explanation

Choice A is correct. Choice A is the correct answer. 1. Isolate the squared term by dividing by 3: $(x - 2)^2 = 4$ . 2. Take the square root: $x - 2 = \pm 2$ . 3. Solve for x: * $x = 2 + 2 = 4$ * $x = 2 - 2 = 0$ Choice B is incorrect because it likely solved $(x-2)^2=16$ (multiplied by 3 instead of dividing? No, $16$ comes from $12 +4$ ? Unclear logic, but wrong). Choice C is incorrect because it forgets to add 2 to the solutions. Choice D is incorrect because it forgets to divide by 3 first.

Key Steps:

•

The correct answer is $x = 4, 0$

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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