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6 February, 14:38

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

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  1. 6 February, 17:17
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    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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