Zeroes of a polynomial function

Algebra Level pending

Consider the following polynomial function:

\[f(x) = x^{n}-2x^{4}-6x^{3}+x^{2}+5x+1\]

If \(n\) is an integer. Which value of \(n\) makes the polynomial function contain the least amount of zeroes?

Find \(nb\), where \(b\) is the least amount of zeroes.

Note: Polynomial functions cannot have negative exponents, that is one of the rules of polynomials.

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