Question

question 18 points 2

solve \\(x^2 - 5x - 24 = 0\\).

\\(x = -6\\) and \\(2\\)

\\(x = -3\\) and \\(8\\)

Explanation:

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<reasoning>

Identify the quadratic equation

\[
x^2 - 5x - 24 = 0
\]

Factor the quadratic trinomial

\[
(x - 8)(x + 3) = 0
\]

Solve for x

\[

$$\begin{aligned} x - 8 = 0 &\implies x = 8 \\ x + 3 = 0 &\implies x = -3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x = -6\) and \(2\)</mcq-option>
<mcq-correct>\(x = -3\) and \(8\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
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]
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</post_analysis>

Answer:

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</pre_analysis>

<reasoning>

Identify the quadratic equation

\[
x^2 - 5x - 24 = 0
\]

Factor the quadratic trinomial

\[
(x - 8)(x + 3) = 0
\]

Solve for x

\[

$$\begin{aligned} x - 8 = 0 &\implies x = 8 \\ x + 3 = 0 &\implies x = -3 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>\(x = -6\) and \(2\)</mcq-option>
<mcq-correct>\(x = -3\) and \(8\)</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
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"Quadratic Equations"
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