2001 AIME I Problems/Problem 3
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, we just need to find the first two terms.
From the Binomial Theorem, the first term of $left(\frac 12-x\right)^{2001}$ (Error compiling LaTeX. ! Extra \right.) is , but , so the first term has in it, not . So we find that term, and the term with .
Applying Vieta's Formulas, we get that the sum of the roots is
See also
2001 AIME I (Problems • Answer Key • Resources) | ||
Preceded by Problem 2 |
Followed by Problem 4 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |