Question

question 10
what are the zeros of the function (f(x) = x^2 - 5x + 6)?
(x = -2, x = -3)
(x = 2, x = 3)
(x = 5, x = 1)
(x = -2, x = 3)

question 11
what are the roots of the function (f(x) = x^2 - 4x + 3)?
(x = -1, x = -4)
(x = 1, x = 3)
(x = -1, x = 3)
(x = -1, x = -3)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Functions"
],
"new_concepts": [
"Zeros of Quadratic Functions",
"Factoring Quadratics"
],
"current_concepts": [
"Quadratic Functions",
"Zeros of Quadratic Functions",
"Factoring Quadratics"
]
}
</pre_analysis>

<reasoning>

Find the zeros of the first quadratic function

\[

$$\begin{aligned} &f(x) = x^2 - 5x + 6 = 0\\ &(x - 2)(x - 3) = 0\\ &x = 2 \quad \text{or} \quad x = 3 \end{aligned}$$

\]

Find the roots of the second quadratic function

\[

$$\begin{aligned} &f(x) = x^2 - 4x + 3 = 0\\ &(x - 1)(x - 3) = 0\\ &x = 1 \quad \text{or} \quad x = 3 \end{aligned}$$

\]
</reasoning>

<answer>

Question 10

<mcq-option>\(x = -2, x = -3\)</mcq-option>
<mcq-correct>\(x = 2, x = 3\)</mcq-correct>
<mcq-option>\(x = 5, x = 1\)</mcq-option>
<mcq-option>\(x = -2, x = 3\)</mcq-option>

Question 11

<mcq-option>\(x = -1, x = -4\)</mcq-option>
<mcq-correct>\(x = 1, x = 3\)</mcq-correct>
<mcq-option>\(x = -1, x = 3\)</mcq-option>
<mcq-option>\(x = -1, x = -3\)</mcq-option>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 2,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Functions"
],
"new_concepts": [
"Zeros of Quadratic Functions",
"Factoring Quadratics"
],
"current_concepts": [
"Quadratic Functions",
"Zeros of Quadratic Functions",
"Factoring Quadratics"
]
}
</pre_analysis>

<reasoning>

Find the zeros of the first quadratic function

\[

$$\begin{aligned} &f(x) = x^2 - 5x + 6 = 0\\ &(x - 2)(x - 3) = 0\\ &x = 2 \quad \text{or} \quad x = 3 \end{aligned}$$

\]

Find the roots of the second quadratic function

\[

$$\begin{aligned} &f(x) = x^2 - 4x + 3 = 0\\ &(x - 1)(x - 3) = 0\\ &x = 1 \quad \text{or} \quad x = 3 \end{aligned}$$

\]
</reasoning>

<answer>

Question 10

<mcq-option>\(x = -2, x = -3\)</mcq-option>
<mcq-correct>\(x = 2, x = 3\)</mcq-correct>
<mcq-option>\(x = 5, x = 1\)</mcq-option>
<mcq-option>\(x = -2, x = 3\)</mcq-option>

Question 11

<mcq-option>\(x = -1, x = -4\)</mcq-option>
<mcq-correct>\(x = 1, x = 3\)</mcq-correct>
<mcq-option>\(x = -1, x = 3\)</mcq-option>
<mcq-option>\(x = -1, x = -3\)</mcq-option>
</answer>

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