Question

the product of two consecutive even integers is 120. find the integers.

smaller integer =

larger integer =

Explanation:

Define variables for consecutive even integers

Using the Consecutive Integer Word Problems knowledge point
Let \(x\) be the smaller even integer.
The next consecutive even integer is \(x + 2\).

Set up the quadratic equation

Using the Consecutive Integer Word Problems knowledge point

$$ x(x + 2) = 120 $$

$$ x^2 + 2x - 120 = 0 $$

Solve the quadratic equation

Using the Solving Quadratic Equations knowledge point

$$
LATEXBLOCK0
$$

Determine the pairs of integers

Using the Consecutive Integer Word Problems knowledge point
If \(x = 10\):
The smaller integer is \(10\), and the larger integer is \(12\).

If \(x = -12\):
The smaller integer is \(-12\), and the larger integer is \(-10\).

Answer:

The product of two consecutive even integers is 120. Find the integers.

smaller integer = <blank>\(10\) or \(-12\)</blank>
larger integer = <blank>\(12\) or \(-10\)</blank>