SOLUTION: the prduct of two consecutive integers is 20. find the integers

Question 168742: the prduct of two consecutive integers is 20. find the integers
Found 3 solutions by jim_thompson5910, Alan3354, Mathtut:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
consecutive integers follow the pattern x, x+1, x+2, etc

So "the prduct of two consecutive integers is 20" translates to

Start with the given equation

Distribute

Subtract 20 from both sides.

Factor the left side (note: if you need help with factoring, check out this solver)

Now set each factor equal to zero:
or

or Now solve for x in each case

So our answers are

or

Which means that the two numbers are

-5 and -4

OR...

4 and 5

Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
Just from thinking about it:
4*5 = 20, and -4 x -5 = 20
--------------
The hard way:
n*(n+1)=20

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=81 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 4, -5. Here's your graph:

If n = 4, n+1 is 5.
If n = -5, n+1 is -4.

Answer by Mathtut(3670)   (Show Source): You can put this solution on YOUR website!
call integers a and a+1
a(a+1)=20

:

so our intergers are -5,-4 and 4,5

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