Keyword Analysis & Research: multiplicity of zeros

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What are multiplicities of zeros?

Multiplicity: The multiplicity of a zero, x = c, is the number of times the factor {eq}(x - c) {/eq} appears in the fully factored form of the polynomial. This is equal to the exponent on the factor.

Is there cubic polynomial that has no zeros?

The function f is continuous because it is the sum or difference of a continuous inverse trig function and a polynomial. Is there a cubic polynomial that has no zeros? No it is not possible for a cubic polynomial function to have no real zeros.

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