Question

The product of two consecutive even integers is 168. How do you find the integers?

Answer 1

12 and 14
-12 and -14

Explanation:

let the first even integer be `x`
So the second consecutive even integer will be `x+2`
Since the given product is 168 ,the equation will be as follows:

`x*(x+2)=168`

`x^2+2*x=168`

`x^2+2*x-168=0`

Your equation is of the form

`a.x^2+b*x+c=0`

Find the discriminat `Delta`

`Delta= b^2-4*a*c`

`Delta=2^2-4*1*(-168)`

`Delta=676`

Since `Delta >0` two real roots exist.

`x=(-b+sqrt(Delta))/(2*a)`

`x'=(-b-sqrt(Delta))/(2*a)`

`x=(-2+sqrt(676))/(2*1)`

`x=12`

`x'=(-2-sqrt(676))/(2*1)`

`x'=-14`

Both roots satisfy the condition being even integers

First possibility : two consecutive positive integers

12 and 14

Second possibility : two consecutive negative integers

-12 and -14