2021 AMC 12A Problems/Problem 12
Revision as of 18:28, 11 February 2021 by Pi is 3.14 (talk | contribs) (→Video Solution pi_is_3.14 (Using Vieta's Formulas & Combinatorics))
Contents
[hide]Problem
All the roots of the polynomial are positive integers, possibly repeated. What is the value of ?
Solution
By Vieta's formulae, the sum of the 6 roots is 10 and the product of the 6 roots is 16. By inspection, we see the roots are 1, 1, 2, 2, 2, and 2, so the function is . Therefore, ~JHawk0224
Video Solution by Hawk Math
https://www.youtube.com/watch?v=AjQARBvdZ20
Video Solution by pi_is_3.14 (Using Vieta's Formulas & Combinatorics)
~ pi_is_3.14
See also
2021 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 11 |
Followed by Problem 13 |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
All AMC 12 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.