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-3 and -20

In order to multiple to a positive number and add to a negative one, both the numbers in question must be negative.

The factors of 60 are:

- 1, 60
- 2, 30
- 3, 20
- 4, 15
- 5, 12
- 6, 10

The third pair listed, 3 and 20, will add up to a positive 23. So all that remains is to make them both negative.

(-20) + (-3) = -23

(-20) * (-3) = 60

Q: What two numbers multiply to 60 and add up to -23?

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There are no two real numbers that do, but two complex numbers do: (3.5 + i 3.5 √23) and (3.5 - i 3.5 √23) If you want them to add to 7 and multiply to -294, then the two real numbers -14 and 21 work. Or if you want them to add to -7 and multiply to -294, then the two real numbers 14 and -21 work. To add to -7 and multiply to 294, the following two complex numbers work: (-3.5 + i 3.5 √23) and (-3.5 - i 3.5 √23)

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There aren't any whole numbers that satisfy these conditions. The only numbers that multiply to 23 are 23 and 1.

There are no two real numbers that do, but two complex numbers do: (3.5 + i 3.5 √23) and (3.5 - i 3.5 √23) If you want them to add to 7 and multiply to -294, then the two real numbers -14 and 21 work. Or if you want them to add to -7 and multiply to -294, then the two real numbers 14 and -21 work. To add to -7 and multiply to 294, the following two complex numbers work: (-3.5 + i 3.5 √23) and (-3.5 - i 3.5 √23)

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