Question

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

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

Explanation:

<pre_analysis>
{
"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"
]
}
</pre_analysis>

<reasoning>

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

\[
x = -3 \text{ and } -4
\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = -3 \text{ and } -4\)</mcq-correct>
<mcq-option>(B) \(x = -3 \text{ and } 4\)</mcq-option>
</answer>

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

Answer:

<pre_analysis>
{
"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"
]
}
</pre_analysis>

<reasoning>

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

\[
x = -3 \text{ and } -4
\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = -3 \text{ and } -4\)</mcq-correct>
<mcq-option>(B) \(x = -3 \text{ and } 4\)</mcq-option>
</answer>

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