Difference between revisions of "2021 AMC 12A Problems/Problem 12"
Pi is 3.14 (talk | contribs) (→Video Solution by Hawk Math) |
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==Video Solution by Hawk Math== | ==Video Solution by Hawk Math== | ||
https://www.youtube.com/watch?v=AjQARBvdZ20 | https://www.youtube.com/watch?v=AjQARBvdZ20 | ||
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| + | == Video Solution pi_is_3.14 (Using Vieta's Formulas & Combinatorics) == | ||
| + | https://youtu.be/5U4MJTo3F5M | ||
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| + | ~ pi_is_3.14 | ||
==See also== | ==See also== | ||
{{AMC12 box|year=2021|ab=A|num-b=11|num-a=13}} | {{AMC12 box|year=2021|ab=A|num-b=11|num-a=13}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 18:28, 11 February 2021
Contents
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 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. 
