Final answer:
The Fundamental Theorem of Algebra indicates that the cubic polynomial f(x) = x^3 - 3x^2 + 4x - 2 has exactly three complex roots. These roots may be real or non-real complex numbers, but there are precisely three based on the theorem.
Step-by-step explanation:
The Fundamental Theorem of Algebra states that every non-constant single-variable polynomial with complex coefficients has as many complex roots as its degree, counting multiple roots multiple times. In the case of the polynomial f(x) = x^3 - 3x^2 + 4x - 2, which is a cubic polynomial (its highest degree term is x^3), there will be exactly three complex roots, which could be real or non-real complex numbers.
This means that the polynomial f(x) can be factored into three linear factors of the form (x - z), where z represents a complex number that could be either real or pure imaginary, or a mix of both. Therefore, by the theorem, we can conclude that there are three complex roots for the given polynomial.