What are two numbers that multiply to get to 4 and add to -5?

Let the two numbers be represented by x and y. Then xy = 4 and x + y = -5.

Solving the first equation for y, we get y = 4/x.

Subbing 4/x for y in the second equation, we get x + 4/x = -5.

Multiplying all three terms by x removes the fractional term:

x^2 + 4 = -5x

Rearranging terms in descending powers of x: x^2 + 5x + 4 = 0

Factoring, (x+1)(x+4)=0, so that x = -1 and x= -4 are roots / solutions.

Note that (-1)(-4) = 4 and that (-1) + (-4) = -5, as required.

Two such numbers are {-1, -4).

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