a polynomial of n degree has zeroes
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it can have only n zeroes because it can't have more than it's degree
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Assuming the polynomial is non-constant and has Real coefficients, it can have up to n Real zeros. If n is odd then it will have at least one Real zero. Since any non-Real Complex zeros will occur in Complex conjugate pairs the possible number of Real roots counting multiplicity is an even number less than n.
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