Question

What are two numbers that add to -1 and multiply to -8

Answer 1

Answer:

  (-1-√33)/2, (-1+√33)/2

Step-by-step explanation:

If one of them is x, then it satisfies ...

  x + -8/x = -1

  x^2 -8 = -x . . . . . multiply by x

  x^2 +x = 8 . . . . . add x+8

  x^2 +x + 1/4 = 8+1/4 . . . . complete the square

  (x +1/2)^2 = 33/4

  x + 1/2 = ±(1/2)√33 . . . . . . take the square root

  x = (-1/2)(1 ± √33) . . . . . . . subtract 1/2

The numbers are approximately ...

  -3.37228, 2.37228