problem

**ohadch** · Nov 7th 2009, 05:10 AM

consider the equation 2z^7-5z^5+z-9=0 .
The equation has 7 zeros. Find the product of these Zeros and their sum .

**tonio** · Nov 7th 2009, 08:25 AM

Originally Posted by ohadch

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 $a_0 + a_1x+...+a_nx^n$ , 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 $-\frac{a_{n-1}}{a_n}$ , and their product equals $(-1)^n\frac{a_0}{a_n}$

Tonio

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