boxofrocks14 boxofrocks14
  • 03-07-2018
  • Mathematics
contestada

Find all of the zeros of the function f(x)=x^3-17x^2+81x-65

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sqdancefan
sqdancefan sqdancefan
  • 11-07-2018
A graph shows the function can be factored as
  f(x) = (x -1)((x-8)² +1)

There is one real root and there are two complex roots. The latter can be found from the vertex form factor:
  (x - 8)² + 1 = 0
  (x - 8)² = -1
  x - 8 = ±√(-1) = ±i
  x = 8 ± i

The zeros of the function are {1, 8-i, 8+i}.
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