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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- Nov 7th 2009, 05:10 AMohadchproblem
consider the equation 2z^7-5z^5+z-9=0 .

The equation has 7 zeros. Find the product of these Zeros and their sum . - Nov 7th 2009, 08:25 AMtonio

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 $\displaystyle (-1)^n\frac{a_0}{a_n}$

Tonio