We need to describe the number and nature of the roots of the given function.
We will see that there are 3 real roots and 2 complex roots.
The given function is:
f(x) = x^5 - 3*x^3 - 2
We can see that this is a polynomial of degree 5, so we can expect to see a maximum of 5 different roots.
The easier way to identify the number and nature of the roots, is by looking at the graph of the given function, the one you can see at the end of the answer.
In the graph you can see 4 points.
The points A, B, and D are intersections with the x-axis, meaning that these are real roots of the function, so we have 3 real roots.
Point C is an inflection point, so there we may have various roots, but because it is not on the x-axis (it is below) we know that it defines complex roots. Particularly, the two roots that we need to complete the 5.
Then we can say that we have 3 real roots and 2 complex roots.
If you want to learn more, you can read:
https://brainly.com/question/2770908
