SOLUTION: find two consequetive even integers whose product equal 120

Question 280358: find two consequetive even integers whose product equal 120
Found 2 solutions by Alan3354, jsmallt9:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
sqrt(120) = about 11, between the 2 numbers.
--> 10 & 12 or -12 & -10
Answer by jsmallt9(3759) (Show Source): You can put this solution on YOUR website!
Let x = the first even integer. Then x+2 = the second even integer. Their product would be x(x+2). This is 120:

Now we solve for x. Start by simplifying the left side:

Since this is a quadratic equation we want one side to be zero. So subtract 120 from each side:

Now we factor (or use the Quadratic Formula):

By the Zero Product Property we know that one of these factors must be zero:
x+12 = 0 or x-10 = 0
Solving these we get:
x = -12 or x = 10
That make the second even integer...
x+2 = -12 + 2 = -10 or x+2 = 10 + 2 = 12

So there are two pairs of consecutive even integers whose product is 120:
-12 and -10 or 10 and 12
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