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Question 1110826: What two numbers multiply to -1232 and add up to 34
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
Since the product is negative, one of the numbers is positive and one negative. So, ignoring signs, we want to find two numbers whose product is 1232 and whose DIFFERENCE is 34.
A general technique for doing this is to find the prime factorization of 1232 and play with the prime factors to try to put them together into the two numbers that you want.
The prime factorization of 1232 is
2*2*2*2*7*11
We know the difference between the two numbers we are looking for is 34. That means either both the numbers are even or both are odd. But with those prime factors of 2, we won't be able to get two odd numbers, so we know both numbers are even.
Then it's just trial and error, possibly guided by some logical reasoning. In the end, the two numbers (still without their signs) are
2*2*2*7 = 56 and 2*11 = 22
Finally, putting the signs back on the numbers, knowing that the sum is positive 34, the two numbers we need are 56 and -22.
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