What are the zeroes of f(x) = x2 − x − 2? (4 points)

x = −2, 1

x = 2, −1

x = −2, −1

x = 2, 1

To find the zeroes of the function \( f(x) = x^2 - x - 2 \), we need to solve the equation \( f(x) = 0 \):

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

This is a quadratic equation, which we can solve by factoring. We look for two numbers that multiply to \(-2\) (the constant term) and add up to \(-1\) (the coefficient of the linear term).

The numbers \(-2\) and \(1\) satisfy these conditions:

\[ (-2) \cdot (1) = -2 \]
\[ (-2) + 1 = -1 \]

So we can factor the quadratic equation as follows:

\[ x^2 - x - 2 = (x - 2)(x + 1) \]

Setting each factor to zero gives the solutions:

\[ x - 2 = 0 \quad \text{or} \quad x + 1 = 0 \]
\[ x = 2 \quad \text{or} \quad x = -1 \]

Therefore, the zeroes of the function \( f(x) = x^2 - x - 2 \) are \( x = 2 \) and \( x = -1 \).

The correct answer is:
\[ x = 2, -1 \]

Would you like more details or have any questions?

Here are 5 numbered questions you might want to ask next:
1. How do you solve a quadratic equation by completing the square?
2. Can you explain the quadratic formula and how to use it?
3. What are the applications of quadratic functions in real life?
4. How do you graph a quadratic function?
5. What is the discriminant of a quadratic equation, and what does it signify?

**Tip:** When factoring quadratic equations, always check if the factors multiply to the constant term and add up to the coefficient of the linear term.

Learn how to find the zeroes of the quadratic function x^2 - x - 2 with step-by-step solutions and explanations. This problem involves factoring a quadratic equation and understanding key algebraic concepts. Suitable for Grades 7-9.

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