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11 July, 16:59

What multiplies to negative 24 and adds to 2

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  1. 11 July, 17:08
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    Let us assume the two numbers to be "x" and "y".

    Then

    xy = - 24

    x = - (24/y)

    And

    x + y = 2

    Putting the value of x from the first equation in the second equation, we get

    x + y = 2

    - (24/y) + y = 2

    - 24 + y^2 = 2y

    y^2 - 2y - 24 = 0

    y^2 - 6y + 4y - 24 = 0

    y (y - 6) + 4 (y - 6) = 0

    (y - 6) (y + 4) = 0

    When

    y - 6 = 0

    y = 6

    Then

    x + y = 2

    x + 6 = 2

    x = 2 - 6

    = - 4

    And when

    y + 4 = 0

    y = - 4

    Then

    x + y = 2

    x - 4 = 2

    x = 2 + 4

    = 6

    So the two unknown numbers are - 4 and 6.
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