3

Set 1: Quadratic Equations (Intermediate)

Explanation

Answer: A

Solve: 3(x2)2=123(x - 2)^2 = 12

A.

x=4,0x = 4, 0

✓ Correct
B.

x=6,2x = 6, -2

C.

x=4,4x = 4, -4

D.

x=2±12x = 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: (x2)2=4(x - 2)^2 = 4. 2. Take the square root: x2=±2x - 2 = \pm 2. 3. Solve for x: * x=2+2=4x = 2 + 2 = 4 * x=22=0x = 2 - 2 = 0 Choice B is incorrect because it likely solved (x2)2=16(x-2)^2=16 (multiplied by 3 instead of dividing? No, 1616 comes from 12+412 +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=4,0x = 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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