Mock AIME 5 2005-2006 Problems/Problem 6

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
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