SOLUTION: How do I do this, The product of two consecutive positive even integers is 120. Find the integers.

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Question 84897This question is from textbook algebra
: How do I do this,
The product of two consecutive positive even integers is 120. Find the integers. This question is from textbook algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=1st #, y=2nd #

Since we have 2 consecutive positive even integers, y=x+2. For instance, if our first number is 2, x=2. That means y=x+2=2+2=4. So we have
xy=x%28x%2B2%29=120 "The product of two consecutive positive even integers is 120"
x%5E2%2B2x=120

x%5E2%2B2x-120=0

Now use the quadratic formula to solve for x
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-120+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-120=484.

Discriminant d=484 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+484+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+484+%29%29%2F2%5C1+=+10
x%5B2%5D+=+%28-%282%29-sqrt%28+484+%29%29%2F2%5C1+=+-12

Quadratic expression 1x%5E2%2B2x%2B-120 can be factored:
1x%5E2%2B2x%2B-120+=+1%28x-10%29%2A%28x--12%29
Again, the answer is: 10, -12. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-120+%29


Since we're only looking for positive numbers, our first number is 10. So our second number is

y=10%2B2=12
So our two numbers are 10 and 12