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ProfessorTo find two numbers that multiply to -120 and add up to 7, we need to first list the factors of -120. The factors of -120 are (-1, 120), (-2, 60), (-3, 40), (-4, 30), (-5, 24), (-6, 20), (-8, 15), (-10, 12). Among these pairs, the numbers that add up to 7 are -8 and 15. Therefore, the two numbers are -8 and 15.
Ah, what a lovely math puzzle! To find two numbers that multiply to -120 and add up to 7, we can think of two numbers that have a difference of 7 and a product of -120. Those numbers are 15 and -8. It's like painting a happy little equation where both numbers can come together in perfect harmony to create a beautiful solution.
Let the numbers be m & n
Hence
mn = -120
m +n = 7
It follows m = 7 - n
Substitute
(7 - n)n = -120
Multiply out the brackets
7n - n^2 = -120
Form a Quadratic Eq'n
n^2 - 7n - 120 = 0
Factor
(n - 15)(n + 8) = 0
Hence n = 15 & m = -8
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