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Is it always true that the zeros of the derivative and the zeros of the polynomial always alternate in location along the horizontal axis?
Morl5001
A zero of the derivative will always appear between two zeroes of the polynomial. However, they do not always alternate. Sometimes two or more zeroes of the derivative will occur between two zeroes of a polynomial. This is often seen with quartic or quintic polynomials (polynomials with the highest exponent of 4th or 5th power).
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