# problem

• Nov 7th 2009, 05:10 AM
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 .
• Nov 7th 2009, 08:25 AM
tonio
Quote:

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