We want to see how many complex roots does the polynomial equation has.
We will see that it has no complex roots.
We know that a polynomial equation of degree N has a maximum of N real roots, and if it has K real roots, then it will have (N - K) complex roots.
To see how many real roots the polynomial has, we can graph it and see how many times it crosses the x-axis.
The polynomial is:
p(x) = 5*x^3 - 4*x + 1
So the degree is 3, meaning that the maximum number of complex roots that it can have is 3.
The graph of the polynomial can be seen below:
There you can see that there are 3 x-intercepts. Then there are 3 real roots.
Then there are no complex roots for the polynomial.
If you want to learn more, you can read:
https://brainly.com/question/17141979
