Mathematics, 13.11.2019 02:31 artemiscrock1350

What multiplies to 14 but adds to negative 4?

Answers: 2

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Xy 14
x + y = -4

x + y = -4
x - x + y = -x - 4
y = -x - 4

xy = 14
x(-x - 4) = 14
  x(-x) - x(4) = 14
-x² - 4x = 14
-x² - 4x - 14 = 0
-1(x²) - 1(4x) - 1(14) = 0
-1(x² + 4x + 14) = 0
-1 -1
x² + 4x + 14 = 0
x = -(4) ± √((4)² - 4(1)(14))
2(1)
x = -4 ± √(16 - 56)
  2
x = -4 ± √(-40)
  2
x = -4 ± 2i√(10)
2
x = -2 ± i√(10)

  x + y = -4
-2 ± i√(10) + y = -4
- (-2 ± i√(10)) - (-2 ± i√(10))
y = -2 ± i√(10)
(x, y) = (-2 ± √(10), -2 ± √(10))

The two numbers that multiply to 14 and add up to -4 are -2 ± i√(10).

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