Cade said:How would I go about approaching this problem?
Given the polynomial:
x^100 - 3x + 2 = 0
Find the sum 1 + x + x^2 + ... + x^99 for each possible value of x.
Cade said:Interesting, thanks, how did you derive that?
coolul007 said:isn't a trivial solution to the equation equal to 1, then then sum would be greater than 3, This is the solution that makes the geometric sum equation impossible as you are dividing by zero.
The sum of the roots of a polynomial is equal to the negative coefficient of the term with one less degree than the highest degree term. For example, in the polynomial 2x3+5x2+3x+1, the sum of the roots is -5.
To find the sum of the roots of a polynomial, you can either use the Vieta's formulas or simply add up all the roots. The Vieta's formulas state that the sum of the roots is equal to the negative coefficient of the term with one less degree than the highest degree term. Alternatively, you can factor the polynomial and add up the roots.
Yes, the sum of the roots of a polynomial can be negative. It is determined by the coefficient of the term with one less degree than the highest degree term. If this coefficient is negative, then the sum of the roots will also be negative.
The sum of the roots of a polynomial is significant because it can give us information about the behavior and characteristics of the polynomial. For example, the sum of the roots can help us determine the number of real roots, the sign changes of the polynomial, and the nature of the roots (real or complex).
No, the sum of the roots of a polynomial is not always an integer. It is determined by the coefficients of the polynomial, which can be any real number. Therefore, the sum of the roots can also be a decimal or a fraction.