What two numbers have a product of -120 and a sum of -41?




To find the answer to "What two numbers have a product of -120 and a sum of -41?" we first state what we know. We are looking for x and y and we know that x • y = -120 and x + y = -41.

Before we keep going, it is important to know that x • y is the same as y • x and x + y is the same as y + x. The two variables are interchangeable. Which means that when we create one equation to solve the problem, we will have two answers.


To solve the problem, we take x + y = -41 and solve it for y to get y = -41 - x. Then, we replace y in x • y = -120 with -41 - x to get this:

x • (-41 - x) = -120

Like we said above, the x and y are interchangeable, therefore the x in the equation above could also be y. The bottom line is that when we solved the equation we got two answers which are the two numbers that have a product of -120 and a sum of -41. The numbers are:

-43.74328
2.74328


That's it! The two numbers that have a product of -120 and a sum of -41 are -43.74328 and 2.74328 as proven below:

-43.74328 • 2.74328 ≈ -120

-43.74328 + 2.74328 = -41

Note: Answers are rounded up to the nearest five decimals if necessary so the answers may not be exact.

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