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Zeros of Functions

Any value of x such that f(x) = 0 is called a zero of the function. Only at the zeros can the function change from being positive to negative or vice versa. However, the function does not have to change at the zeros. What is important is the order of the zero. If x = a is a zero of f, and f can be written as a product of factors with tex2html_wrap_inline212 as one of the factors, then the value of n will tell you whether the function changes sign at that zero. If n is odd, the sign changes, if it is even, the sign remains the same. As an example, notice that tex2html_wrap_inline218 . Thus, the function has a zero at x = 0. Since n = 2 in this case, the zero is even and the sign does not change.



Vector Calculus
Wed Sep 17 14:50:13 MST 1997