https://file.aiquickdraw.com/mathbot/file/1726790456314shskwivz.jpg

The equation provided is \( x^2 - 2x - 24 = 0 \). Let's solve this quadratic equation to find its roots.

### Step 1: Identify the coefficients
The equation is in standard form \( ax^2 + bx + c = 0 \), where:
- \( a = 1 \)
- \( b = -2 \)
- \( c = -24 \)

### Step 2: Use the quadratic formula
The quadratic formula is:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

Substitute the values of \( a \), \( b \), and \( c \) into the formula:

\[
x = \frac{-(-2) \pm \sqrt{(-2)^2 - 4(1)(-24)}}{2(1)}
\]
\[
x = \frac{2 \pm \sqrt{4 + 96}}{2}
\]
\[
x = \frac{2 \pm \sqrt{100}}{2}
\]
\[
x = \frac{2 \pm 10}{2}
\]

### Step 3: Solve for the two possible values of \( x \)

1. \( x = \frac{2 + 10}{2} = \frac{12}{2} = 6 \)
2. \( x = \frac{2 - 10}{2} = \frac{-8}{2} = -4 \)

### Step 4: Conclusion
The roots of the equation are \( x = 6 \) and \( x = -4 \). Therefore, the correct answer is the option \( \{-4, 6\} \), which matches the selected option in the image.

Would you like further details on this solution? Here are 5 questions for further exploration:

1. How do we determine the discriminant of a quadratic equation?
2. Can we solve this quadratic equation by factoring instead of using the quadratic formula?
3. What does it mean geometrically to find the roots of a quadratic equation?
4. How would the graph of \( x^2 - 2x - 24 \) look, and where would the roots be located on the x-axis?
5. Can quadratic equations always be solved using the quadratic formula?

**Tip:** When solving a quadratic equation, always check if the discriminant \( b^2 - 4ac \) is a perfect square for simple factorization.

What are the roots of the equation x^2 - 2x - 24 = 0?

Learn how to solve the quadratic equation x^2 - 2x - 24 = 0 step-by-step using the quadratic formula. This problem is ideal for students in Grades 8-10 and covers key algebra concepts, including solving for roots and understanding the quadratic formula.

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