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  1. #1
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    problem

    consider the equation 2z^7-5z^5+z-9=0 .
    The equation has 7 zeros. Find the product of these Zeros and their sum .
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  2. #2
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    Quote Originally Posted by ohadch View Post
    consider the equation 2z^7-5z^5+z-9=0 .
    The equation has 7 zeros. Find the product of these Zeros and their sum .

    For any polynomial $\displaystyle a_0 + a_1x+...+a_nx^n$, Vieta's formulas (which are usually studied in high school but mainly for the quadratic equation. Their generalization for any degree is a nice exercise in symmetric polynomials) tell us that the sum of its roots equals $\displaystyle -\frac{a_{n-1}}{a_n}$, and their product equals $\displaystyle (-1)^n\frac{a_0}{a_n}$

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