# How do you find the two consecutive even integers whose product is 840?

##### 2 Answers

Translate the problem to an algebraic statement and solve a quadratic equation to find that there are two pairs of numbers that satisfy the problem.

#### Explanation:

When we are solving algebraic problems, the first thing we must do is define a variable for our unknowns. Our unknowns in this problem are two consecutive even numbers whose product is

We are told that the product of these numbers is

Distributing the

Subtracting

Now we have a quadratic equation. We can try to factor it, by finding two numbers that multiply to

Our solutions are:

Thus, we have two combinations:

#28# and#28+2# , or#30# . You can see that#28*30=840# .#-30# and#-30+2# , or#-28# . Again,#-30*-28=840# .

The reqd. nos. are

#### Explanation:

Suppose that the reqd. integers are

By given, then, we have

**CASE I**

**Case II**