2015 AMC 10B Problems/Problem 14
Contents
[hide]Problem
Let , , and be three distinct one-digit numbers. What is the maximum value of the sum of the roots of the equation ?
Solution 1
Expanding the equation and combining like terms results in . By Vieta's formula the sum of the roots is . To maximize this expression we want to be the largest, and from there we can assign the next highest values to and . So let , , and . Then the answer is .
Solution 2
Factoring out from the equation yields . Therefore the roots are and . Because must be the larger root to maximize the sum of the roots, letting and be and respectively yields the sum .
Video Solution 1
~Education, the Study of Everything=
Video Solution 2
~savannahsolver
See Also
2015 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.