Difference between revisions of "2021 Fall AMC 12A Problems/Problem 15"
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− | + | For a certain complex number <math>A,</math> the roots <math>z_1,</math> <math>z_2,</math> <math>z_3</math> of | |
− | + | <cmath>z^3 + Az^2 + (25 + 30i) z - 125i = 0</cmath>satisfy <math>|z_1| = |z_2| = |z_3|.</math> Find <math>A.</math> | |
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==Solution== | ==Solution== |
Revision as of 16:49, 24 May 2023
For a certain complex number the roots
of
satisfy
Find
Solution
By Vieta's formulas, , and
Since
Since
Also, and
Our answer is
~kingofpineapplz
See Also
2021 Fall AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 14 |
Followed by Problem 16 |
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 12 Problems and Solutions |
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