1982 AHSME Problems/Problem 27
Problem
Suppose is a solution of the polynomial equation where and are real constants and Which of the following must also be a solution?
Solution
Let so the given polynomial equation becomes Note that is a polynomial equation in with real coefficients.
We are given that is a solution to By the Complex Conjugate Root Theorem, we conclude that must also be a solution to from which must also be a solution to the given polynomial equation.
~MRENTHUSIASM
See Also
1982 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.