What two integers have a sum of -17 and product of 52

Answer 1

X + Y = -17

XY = 52

Now, solve for X in first equation:

X = -17 - Y

Now, substitute into 2nd equation:

(-17 - Y)(Y) =

-17Y - YY = 52

YY + 17Y +52 = 0

(Y + 13)(Y + 4) = 0

Y = -13, -4

Answer 2

Let the two integers be a and b.

"sum of -17" means a + b = -17 [eq1]

"product of 52" means ab = 52 [eq2]

Solving by finding prime factors:

Prime factors of 52 are: 2, 2, 13

The way to get a sum of -17 by grouping those prime factors is (-(2)(2)) + (-13).

The integers are -4 and -13.

Check:

Is sum -17: (-4) + (-13) = -17 ?

-17 = -17 ?yes

Is product 52 (-4)*(-13) = 52 ?

52 = 52 ?yes

Answer 3

Steps to find answer.

1) Ask yourself the following question first:

What is the definition of an integer?

2) Ok now that you know what an integer is this will narrow down which 2 numbers when multiplied (to get the product will equal 52).

Here is one way to quickly narrow down the options. To get to the answer we should think about the following:

1. 2A) Ask yourself what integers can you divide 52 by? Those two numbers when multiplied by each other will then give you a product of 52
2. 2B) If I get a positive number, 52 when multiplying these two integers and a negative number when the two integers are added what does this mean about the two number in regards to the signs (+ /_)of each individual integer?
3. 3B) Well in order to get a negative number for the sum (-17) and a positive number when multiplying, this means BOTH of the numbers must be negative.
4. Why? when you multiply two negative numbers you get a positive number. This is not true when you multiple a negative and a positive number. Thus they both have to be negative numbers.
5. Basic example of this = integers (-2, -3)
6. -2 x -3 = 6 (product of two negative numbers)
7. -2 +-3 = -5 (sum of two negative numbers)

4B)) In summary we now know we need the following: a) both numbers must be negative numbers to get a sum of (-17) and a product of 52.

1. Lets forget about the (- ) sign for a moment and go back to thinking what POSITIVE integers are divisible by 52. We then can change them to negative numbers so that when multiplied, they still = 52 and when added they have a sum of -17
2. OK what integers can you divide 52 by?

---Results/possibilities:

52 / 2 = 26 (Yes they integers)

52/4 = 13 (yes these are integers)

52/5 = 10.4 (not an integer).

-Ok now now lets change the signs of these numbers, may both of them negative and figure out what gives us a sum of -17 when added.

Ok 2 x 26 = 52 -----Change to negative integers: -2 x -26 = 52 ; now lets try adding them. -2 + -26 = -28 (NOPE NOTE THE ANSWER)

Now lets try 4 and 13: 4 x 13 = 52, lets change then to negative numbers: -4 x -13 = 52; NOW LETS try ADDING the TWO: -4 + -13 = -17 YEAH we have an answer.....!

Answer: -4 x -13 are the two integers that have a product of 52 and a sum of -17!