# Nakafa Framework: LLM

URL: https://nakafa.com/en/exercises/high-school/snbt/quantitative-knowledge/try-out/set-5/15

Exercises: Try Out - Set 5: Real exam simulation to sharpen your skills and build confidence. - Problem 15

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## Exercise 15

### Question

export const metadata = {
  title: "Problem 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

An equation is expressed in the form <InlineMath math="\begin{vmatrix} x^2 & x \\ 2 & 1 \end{vmatrix} = 8" />. The possible values of <InlineMath math="x" /> are...


### Choices

- [x] $$4 \text{ or } -2$$
- [ ] $$-4 \text{ or } 2$$
- [ ] $$-2 \text{ or } 3$$
- [ ] $$2 \text{ or } -3$$
- [ ] $$3 \text{ or } 8$$

### Answer & Explanation

export const metadata = {
  title: "Solution to Problem 15",
  authors: [{ name: "Nabil Akbarazzima Fatih" }],
  date: "12/23/2025",
};

Given the matrix determinant equation <InlineMath math="\begin{vmatrix} x^2 & x \\ 2 & 1 \end{vmatrix} = 8" />.

Recall that the determinant of a <InlineMath math="2 \times 2" /> matrix is the difference between the product of the main diagonal and the secondary diagonal: <InlineMath math="\begin{vmatrix} a & b \\ c & d \end{vmatrix} = ad - bc" />.

So, we expand the equation:
<MathContainer>
  <BlockMath math="(x^2)(1) - (x)(2) = 8" />
  <BlockMath math="x^2 - 2x = 8" />
</MathContainer>

Move all terms to the left side to form a quadratic equation:
<MathContainer>
  <BlockMath math="x^2 - 2x - 8 = 0" />
</MathContainer>

Factor the quadratic equation. We look for two numbers that multiply to <InlineMath math="-8" /> and add up to <InlineMath math="-2" />. These numbers are <InlineMath math="-4" /> and <InlineMath math="2" />.
<MathContainer>
  <BlockMath math="(x - 4)(x + 2) = 0" />
</MathContainer>

The zeros are:
<MathContainer>
  <BlockMath math="x - 4 = 0 \Rightarrow x = 4" />
  <BlockMath math="x + 2 = 0 \Rightarrow x = -2" />
</MathContainer>

So, the possible values of <InlineMath math="x" /> are <InlineMath math="4" /> or <InlineMath math="-2" />.


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