which equations are true for $x = -2$ and $x = 2$? select two options

$x^2 - 4 = 0$

$x^2 = -4$

$3x^2 + 12 = 0$

$4x^2 = 16$

$2(x - 2)^2 = 0$

Question

which equations are true for $x = -2$ and $x = 2$? select two options

$x^2 - 4 = 0$

$x^2 = -4$

$3x^2 + 12 = 0$

$4x^2 = 16$

$2(x - 2)^2 = 0$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Evaluating Equations", "Quadratic Roots" ], "current_concepts": [ "Quadratic Equations", "Evaluating Equations", "Quadratic Roots" ] } ## Evaluate the first equation $$ \begin{aligned} &\text{For } x = -2: (-2)^2 - 4 = 4 - 4 = 0 \quad (\text{True})\ &\text{For } x = 2: (2)^2 - 4 = 4 - 4 = 0 \quad (\text{True}) \end{aligned} $$ ## Evaluate the second and third equations $$ \begin{aligned} &x^2 = -4 \implies (\pm 2)^2 = 4 e -4 \quad (\text{False})\ &3x^2 + 12 = 0 \implies 3(\pm 2)^2 + 12 = 12 + 12 = 24 e 0 \quad (\text{False}) \end{aligned} $$ ## Evaluate the fourth and fifth equations $$ \begin{aligned} &4x^2 = 16 \implies 4(\pm 2)^2 = 4(4) = 16 \quad (\text{True})\ &2(x-2)^2 = 0 \implies 2(-2-2)^2 = 32 e 0 \quad (\text{False}) \end{aligned} $$

(A) $x^2 - 4 = 0$

(B) $x^2 = -4$

(C) $3x^2 + 12 = 0$

(D) $4x^2 = 16$

(E) $2(x - 2)^2 = 0$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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Question

Explanation:

Evaluate the first equation

Evaluate the second and third equations

Evaluate the fourth and fifth equations

Answer: