2015 AMC 10B Problems/Problem 14
Contents
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
.
See Also
2015 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AMC 10 Problems and Solutions |
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