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How many zeroes at the most can a polynomial of degree 'n' have?

Question

How many zeroes at the most can a polynomial of degree 'n' have?

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Solution 1

A polynomial of degree 'n' can have at most 'n' zeroes. This is based on the Fundamental Theorem of Algebra, which states that a polynomial of degree 'n' has exactly 'n' roots, or zeroes, in the complex number system. However, not all of these roots are necessarily distinct or real. If we only consider real zeroes, the number can be less than 'n', but it cannot be more. Therefore, the maximum number of zeroes a polynomial of degree 'n' can have is 'n'.

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Solution 2

A polynomial of degree 'n' can have at most 'n' zeroes. This is based on the Fundamental Theorem of Algebra which states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes real numbers as a subset of the complex numbers. Therefore, a polynomial of degree 'n' can have up to 'n' complex roots, or zeroes.

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