solve the quadratic equation: (x^2 + 7x + 12 = 0)

(x = -3) and (-4)
(x = -3) and (4)

Question

solve the quadratic equation: (x^2 + 7x + 12 = 0)

(x = -3) and (-4)
(x = -3) and (4)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Factoring Quadratic Trinomials" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Factoring Quadratic Trinomials" ] } ## Factor the quadratic trinomial $$ x^2 + 7x + 12 = (x + 3)(x + 4) $$ ## Set each factor to zero $$ \begin{aligned} x + 3 &= 0 \implies x = -3 \ x + 4 &= 0 \implies x = -4 \end{aligned} $$ ## Identify the matching option $$ x = -3 \text{ and } -4 $$

(A) $x = -3 \text{ and } -4$

(B) $x = -3 \text{ and } 4$

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

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QUESTION IMAGE

Question

Explanation:

Factor the quadratic trinomial

Set each factor to zero

Identify the matching option

Answer: