Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 6"

Latest revision as of 20:17, 8 October 2014

$P_1$ , $P_2$ , and $P_3$ are polynomials defined by:

$P_1(x) = 1+x+x^3+x^4+\cdots+x^{96}+x^{97}+x^{99}+x^{100}$

$P_2(x) = 1-x+x^2-\cdots-x^{99}+x^{100}$

$P_3(x) = 1+x+x^2+\cdots+x^{66}+x^{67}$

Find the number of distinct complex roots of $P_1 \cdot P_2 \cdot P_3$ .

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 == Problem ==
+<math>P_1</math>, <math>P_2</math>, and <math>P_3</math> are polynomials defined by:
+: <math>P_1(x) = 1+x+x^3+x^4+\cdots+x^{96}+x^{97}+x^{99}+x^{100}</math>
+: <math>P_2(x) = 1-x+x^2-\cdots-x^{99}+x^{100}</math>
+: <math>P_3(x) = 1+x+x^2+\cdots+x^{66}+x^{67}</math>
+Find the number of distinct complex roots of <math>P_1 \cdot P_2 \cdot P_3</math>.
+== Solution ==
 == Solution ==