7

Set 17: Quadratic Equations

Explanation

Answer: B

Solve: 3x212=03x^2 - 12 = 0

A.

x=2x = 2

B.

x=±2x = \pm 2

✓ Correct
C.

x=±4x = \pm 4

D.

x=±12x = \pm \sqrt{12}

Detailed Explanation

Choice B is correct. Choice B is the correct answer. 1. Factor out the GCF of 3: 3(x24)=03(x^2 - 4) = 0. 2. Divide by 3: x24=0x^2 - 4 = 0. 3. Factor difference of squares: (x2)(x+2)=0(x - 2)(x + 2) = 0. 4. Solve: x=2x = 2 or x=2x = -2. Alternatively, isolate x2x^2: 3x2=12x2=4x=±23x^2 = 12 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2. Choice A is incorrect because it misses the negative solution. Choice C is incorrect because it forgets to take the square root of 4. Choice D is incorrect because it forgets to divide by 3 first.

Key Steps:

The correct answer is x=±2x = \pm 2

Why others are wrong:
A: Choice A 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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