1966 AHSME Problems/Problem 30
Problem
If three of the roots of are , , and then the value of is:
Solution
Since this is a quartic equation, there are going to be solutions. By Vieta's formulas, since the term is , the sum of the roots is also . Therefore, the 4th root of this polynomial is . Lastly, by Vieta's Formulas,
See also
1966 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 29 |
Followed by Problem 31 | |
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.