# The sum and product of an nth degree polynomial

by phyguy321
Tags: degree, polynomial, product
 P: 45 1. The problem statement, all variables and given/known data Suppose f(x) $$\in$$ Complex[x] is a monic polynomial of degree n with roots c1,c2,...cn. Prove that the sum of the roots is -a$$_{n-1}$$ and their product is (-1)$$^{n}$$a$$_{0}$$ 2. Relevant equations 3. The attempt at a solution (x-c1)(x-c2)...(x-cn) = x$$^{n}$$ + (c1+c2+...+cn)x$$^{n-1}$$....(c1*c2*....*cn) I just need a realistic proof this assumes too much
 Sci Advisor HW Helper Thanks P: 25,251 In what way do you think that's assuming too much? Do you know the Fundamental Theorem of Algebra?
 P: 45 but how do i know that (x-c1)(x-c2)...(x-cn) = xLaTeX Code: ^{n} + (c1+c2+...+cn)xLaTeX Code: ^{n-1} ....(c1*c2*....*cn)?
 Sci Advisor HW Helper Thanks P: 25,251 The sum and product of an nth degree polynomial Count powers of x. There's only one way to make x^n and x^0. There are n ways to make x^1. You just imagine multiplying it out.
Math
Emeritus