The product of two consecutive positive integers is 42. Write and solve a quadratic equation to find the solutions. Then show how you use those solutions to find the two consecutive positive integers.

Solution

T h e p ro d u c t o f tw o co n sec u t i v e p os i t i v e in t e g ers i s 42. W r i t e an d so l v e a q u a d r a t i c e q u a t i o n t o f in d t h e so l u t i o n s . T h e n s h o w h o w yo u u se t h ose so l u t i o n s t o f in d t h e tw o co n sec u t i v e p os i t i v e in t e g ers .

The numbers : 6, 7

Solution steps

Represent the numbers with

x

First number : x

Consecutive number : x + 1

A.T.Q.:

x (x + 1) = 42

Solve

x (x + 1) = 42 : x = 6, x = - 7

Select positive solutions:

6

x + 1 = 6 + 1 = 7

The numbers : 6, 7