2007 Alabama ARML TST Problems/Problem 12
Problem
If and , then evaluate
Express your answer as a fraction in lowest terms.
Solution
For all :
is a root of .
is a root of .
is a root of .
is a root of , since .
Since the degree of is , has exactly roots. So, the problem is asking for the sum of the roots of .
Using the Binomial Theorem, .
So, .
Therefore, by Vieta's Formulas, the sum of the roots of is .
See also
2007 Alabama ARML TST (Problems) | ||
Preceded by: Problem 11 |
Followed by: Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 |