Question

question 19 points 2

solve \\(x^2 - 2x - 15 = 0\\)

\\(x = -5, -3\\)

\\(x = 5, -3\\)

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>

Identify the quadratic equation

\[
x^2 - 2x - 15 = 0
\]

Factor the quadratic trinomial

\[
(x - 5)(x + 3) = 0
\]

Solve for x

\[

$$\begin{aligned} x - 5 = 0 &\implies x = 5 \\ x + 3 = 0 &\implies x = -3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x = -5, -3\)</mcq-option>
<mcq-correct>\(x = 5, -3\)</mcq-correct>
</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>

Identify the quadratic equation

\[
x^2 - 2x - 15 = 0
\]

Factor the quadratic trinomial

\[
(x - 5)(x + 3) = 0
\]

Solve for x

\[

$$\begin{aligned} x - 5 = 0 &\implies x = 5 \\ x + 3 = 0 &\implies x = -3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x = -5, -3\)</mcq-option>
<mcq-correct>\(x = 5, -3\)</mcq-correct>
</answer>

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