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Mock AIME 5 2005-2006 Problems/Problem 6

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Problem

$P_1$, $P_2$, 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 $P_1 \cdot P_2 \cdot P_3$.

Solution

Solution

See also

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by
Problem 5 		Followed by
Problem 7
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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