The Fundamental Theorem of Algebra states that a non-constant polynomial of degree \( n \) has exactly \( n \) roots (or zeros), counting multiplicities, in the complex number system.
For the polynomial \( f(x) = 7x^6 - 5x^5 + x \), the degree is determined by the highest power of \( x \) present in the polynomial.
In this case, the highest power of \( x \) is \( 6 \) (from the term \( 7x^6 \)), which means that \( f(x) \) is a polynomial of degree \( 6 \).
Thus, according to the Fundamental Theorem of Algebra, the greatest number of zeros that the polynomial \( f(x) \) can have is \( 6 \).
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