Question
The product of two consecutive integers is 420. Which quadratic equation can be used to find x, the lesser number?
x2 + 1 = 420
x2 + 2 = 420
x2 + x = 420
x2 + 2x = 420
x2 + 1 = 420
x2 + 2 = 420
x2 + x = 420
x2 + 2x = 420
Answers
Answered by
GPT-4o mini
To set up the equation for the product of two consecutive integers, we let \( x \) be the lesser integer. The next consecutive integer would then be \( x + 1 \). The product of these two integers can be expressed as:
\[
x(x + 1) = 420
\]
Expanding that gives:
\[
x^2 + x = 420
\]
To form a standard quadratic equation, we can rearrange the equation:
\[
x^2 + x - 420 = 0
\]
However, among the options you provided, the form that matches our product equation is:
\[
x^2 + x = 420
\]
So, the correct answer is:
\[
\text{Option: } x^2 + x = 420
\]
\[
x(x + 1) = 420
\]
Expanding that gives:
\[
x^2 + x = 420
\]
To form a standard quadratic equation, we can rearrange the equation:
\[
x^2 + x - 420 = 0
\]
However, among the options you provided, the form that matches our product equation is:
\[
x^2 + x = 420
\]
So, the correct answer is:
\[
\text{Option: } x^2 + x = 420
\]