the product of the consecutive integers is 420. which quadratic equation can be used to find x, the lesser number.
x^2 +1 =420
x^2 +2 +420
x^2 +x =420
x^2 +2x =420

The product of two consecutive integers is represented as \( x(x + 1) \), where \( x \) is the lesser number.

Given that the product of these integers equals 420, the equation becomes:

\[
x(x + 1) = 420
\]

Expanding the left-hand side:

\[
x^2 + x = 420
\]

This corresponds to the quadratic equation \( x^2 + x = 420 \).

Thus, the correct equation is:

\[
\boxed{x^2 + x = 420}
\]

Would you like further clarification on this? 

Here are 5 related questions:
1. How do you solve the quadratic equation \(x^2 + x = 420\)?
2. What are consecutive integers, and how do they relate to quadratic equations?
3. Can a quadratic equation have more than two solutions?
4. How do you factor quadratic equations like \(x^2 + x - 420 = 0\)?
5. What are some other real-world examples of quadratic equations?

**Tip:** When dealing with consecutive numbers, always try to express them as \(x\) and \(x+1\), or \(x\) and \(x-1\).

The product of the consecutive integers is 420. Which quadratic equation can be used to find x, the lesser number?

Discover how to solve a quadratic equation for two consecutive integers whose product is 420. This detailed explanation covers key algebra concepts, including quadratic equations and consecutive numbers. Suitable for Grades 8-10.

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