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MATH / There exists a polynomial P of degree 5 with the following property: If z is a complex number such that z⁵+2004z=1, then P(z²)=0. Calculate (P(1))/(P(−1)).

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problem

There exists a polynomial PP of degree 5 with the following property: If zz is a complex number such that z5+2004z=1,z^5 + 2004z = 1, then P(z2)=0.P(z^2) = 0. Calculate P(1)P(−1).\frac{P(1)}{P(-1)}.
Plain-text mathematical notation (without MathML)
There exists a polynomial P of degree 5 with the following property: If z is a complex number such that z⁵+2004z=1, then P(z²)=0.  Calculate
(P(1))/(P(−1)).
Original LaTeX notation
There exists a polynomial $P$ of degree 5 with the following property: If $z$ is a complex number such that $z^5 + 2004z = 1,$ then $P(z^2) = 0.$  Calculate
\[\frac{P(1)}{P(-1)}.\]

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
dc21c61f-f63e-5464-a31b-be7f750d5fc5
task_key
intermediate~5falgebra--test--dc21c61f-f63e-5464-a31b-be7f750d5fc5
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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