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Answer :
To find the greatest number of zeros a polynomial can have, we need to look at the degree of the polynomial. The degree of a polynomial is the highest power of the variable in the expression.
In the polynomial [tex]\( f(x) = 7x^6 - 5x^5 + x \)[/tex], the highest power of [tex]\( x \)[/tex] is 6. This means that the degree of the polynomial is 6.
The maximum number of zeros (or roots) a polynomial can have is equal to its degree. Therefore, since the degree of [tex]\( f(x) \)[/tex] is 6, the greatest number of zeros this polynomial could have is 6.
Thus, the answer is 6 zeros.
In the polynomial [tex]\( f(x) = 7x^6 - 5x^5 + x \)[/tex], the highest power of [tex]\( x \)[/tex] is 6. This means that the degree of the polynomial is 6.
The maximum number of zeros (or roots) a polynomial can have is equal to its degree. Therefore, since the degree of [tex]\( f(x) \)[/tex] is 6, the greatest number of zeros this polynomial could have is 6.
Thus, the answer is 6 zeros.
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