What two numbers multiply together and equal 16 and add together and equal -2?

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Mathematics

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What two numbers multiply together and equal 16 and add together and equal -2?

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Joannashuttid Joannashuttid · Answer 1

Joannashuttid Joannashuttid

None, because both numbers must be negative in order to get a positive answer, or both positive. However, -2 means that there is at least one negative number, or two negative numbers. the only option : -1+(-1)= -2. So there is no real solution.

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AL2006id AL2006id · Answer 2

There is a solution, but you might not have learned how to do it yet
in middle school.

If you've learned to use the quadratic formula to solve a quadratic equations,
then you can do this.

The first requirement says: ' x ' times ' y ' = 16
The second requirement says: (x + y) = -2

Take the second requirement, and subtract ' x ' from each side:

y = -x - 2

Substitute this into the first requirement:

' x ' times (-x - 2) = 16

Eliminate parentheses:

-x² - 2x = 16

Subtract 16 from each side:

-x² - 2x - 16 = 0

Multiply each side by -1:

x² + 2x + 16 = 0

Solve this with the quadratic formula, and you get two solutions,
which are the two numbers that satisfy both requirements.

The numbers are

-1 + √-15

-1 - √-15

Check:

-- Product: (-1 + √-15) times (-1 - √-15) = 1 + 15 = 16

-- Sum = -1 + √-15 -1 - √-15 = -2

They work.
yay