https://file.aiquickdraw.com/mathbot/file/1730395342555z1ogm0bn.jpg

Let's examine your work.

The problem states that two numbers have:
1. A sum of \( 1 \).
2. A product of \( -42 \).

To form a single-variable quadratic equation with these values, we can let the numbers be \( x \) and \( y \). Then:

- The sum is \( x + y = 1 \).
- The product is \( xy = -42 \).

We can express \( y \) in terms of \( x \) by rearranging the sum equation:
\[
y = 1 - x
\]

Next, substitute \( y = 1 - x \) into the product equation:
\[
x(1 - x) = -42
\]

Expanding this, we get:
\[
x - x^2 = -42
\]
or equivalently,
\[
x^2 - x - 42 = 0
\]

This is the quadratic equation in standard form: 
\[
x^2 - x - 42 = 0
\]

**Conclusion**: The correct equation is \( x^2 - x - 42 = 0 \), not \( x^2 + 1x - 42 \).

Would you like more details or have any questions?

---

Here are 5 related questions to deepen your understanding:

1. How do we use the sum and product of roots to form a quadratic equation?
2. Why is it necessary to rewrite the equation in standard form?
3. What methods can be used to solve the equation \( x^2 - x - 42 = 0 \)?
4. How can we verify the roots of this equation once found?
5. What is the significance of having a negative product in this context?

**Tip**: Remember, when you know the sum and product of two roots, you can always create a quadratic equation in the form \( x^2 - (\text{sum of roots})x + (\text{product of roots}) = 0 \).

Is this right? Two numbers have a sum of 1 and a product of -42. What single-variable quadratic equation in standard form can be used to represent the product of the numbers?

Learn how to form a quadratic equation given the sum of 1 and product of -42 for two numbers. This problem explores algebraic concepts related to quadratic equations and is ideal for Grades 7-9.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation