Difference between revisions of "2004 AMC 12B Problems/Problem 17"
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<cmath>8(x-x_1)(x-x_2)(x-x_3) = 8x^3 + 4ax^2 + 2bx + a</cmath> | <cmath>8(x-x_1)(x-x_2)(x-x_3) = 8x^3 + 4ax^2 + 2bx + a</cmath> | ||
gives us that <math>a = -8x_1x_2x_3 = -256 \Rightarrow \mathrm{(A)}</math>. | gives us that <math>a = -8x_1x_2x_3 = -256 \Rightarrow \mathrm{(A)}</math>. | ||
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+ | ==Video Solution== | ||
+ | https://youtu.be/40mJNmstTEY | ||
== See also == | == See also == |
Revision as of 16:25, 3 January 2020
Contents
Problem
For some real numbers and , the equation has three distinct positive roots. If the sum of the base- logarithms of the roots is , what is the value of ?
Solution
Let the three roots be . By Vieta’s formulas, gives us that .
Video Solution
See also
2004 AMC 12B (Problems • Answer Key • Resources) | |
Preceded by Problem 16 |
Followed by Problem 18 |
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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