How many roots does have?

  5

Step-by-step explanation:

The fundamental theorem of algebra tells you a 5th-degree polynomial has 5 roots. This one has 3 real roots and two complex roots. They are ...

  x = 0

  x = 1 (multiplicity 2)

  x = -1 -i√2

  x = -1 +i√2

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The graph shows the three real roots and the graph of the remaining factor after those roots are factored out. It is easy to find the complex roots of that factor from its vertex.