2001 AIME I Problems/Problem 3
From AoPSWiki
Problem
Find the sum of the roots, real and non-real, of the equation 
, given that there are no multiple roots.
Solution
From Vieta's formulas, in a polynomial of the form 
, then the sum of the roots is 
.
From the Binomial Theorem, the first term of 
is 
, but 
, so the term with the largest degree is 
. So we need the coefficient of that term, as well as the coefficient of 
.
Applying Vieta's formulas, we find that the sum of the roots is 
.
See also
| 2001 AIME I (Problems • Resources) | ||
| Preceded by Problem 2 | Followed by Problem 4 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
