Final answer:
The polynomial f(x) = -2x^4 + 5x^3 - 4x^2 + x has four roots because the degree of the polynomial is 4, as determined by the highest power of x.
Step-by-step explanation:
The polynomial in question is f(x) = -2x^4 + 5x^3 - 4x^2 + x. The number of roots a polynomial should have is equal to its degree. The degree of a polynomial is the highest power of x that appears in the polynomial. Since the highest power in the given polynomial is 4 (from the term -2x^4), this polynomial should have 4 roots. This follows from the Fundamental Theorem of Algebra, which states that every non-constant single-variable polynomial with complex coefficients has as many roots as its degree, including multiple roots and complex roots.