What adds to equal minus 4 and multiplies to equal 5?

Answer 1

No pairs of integers solve those equations.

Since sqrt 5 > sqrt 4, the addition requires that one of the numbers is negative and the other positive, so they can have no positive product 5. There are complex (imaginary) solutions.

x + y = -4

x * y = 5

Substituting x for y

x (-x-4) = 5

-x2 - 4x - 5 = 0

x2 + 4x + 5 = 0

There are no integer solutions. The complex solutions are

x = [-1+2i]/2 or [-1-2i]/2 where i = sqrt (-1)

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Note that if the values are reversed

x + y = -5

x * y = 4

the answer is the pair (-1, -4)