Скачать или смотреть Multiplicity of zeros of polynomials | Polynomial graphs | Algebra 2 | Khan Academy

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The polynomial p(x)=(x-1)(x-3)² is a 3rd degree polynomial, but it has only 2 distinct zeros. This is because the zero x=3, which is related to the factor (x-3)², repeats twice. This is called multiplicity. It means that x=3 is a zero of multiplicity 2, and x=1 is a zero of multiplicity 1. Multiplicity is a fascinating concept, and it is directly related to graphical behavior of the polynomial around the zero.

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