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Select all that are always true of a function that has no real roots: (2 points)

Responses

the solutions are irrational numbers
the solutions are irrational numbers

the graph does not touch the x-axis
the graph does not touch the x-axis

the graph does not touch the y-axis
the graph does not touch the y-axis

the solutions are complex numbers

1 answer

For a function that has no real roots, the following statements are always true:

  1. The graph does not touch the x-axis.
  2. The solutions are complex numbers.

The other statements about the solutions being irrational numbers or the graph not touching the y-axis are not necessarily true.

In summary, the correct selections are:

  • the graph does not touch the x-axis
  • the solutions are complex numbers