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MATH / Let p be an integer, and let the roots of

Problem

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problem

Let pp be an integer, and let the roots of f(x)=x4−6x3+26x2+px+65f(x) = x^4 - 6x^3 + 26x^2 + px + 65be ak+ibka_k + ib_k for k=1,k = 1, 2,2, 3,3, 4.4. Given that the ak,a_k, bkb_k are all integers, and that none of the roots are real, find p.p.
Plain-text mathematical notation (without MathML)
Let p be an integer, and let the roots of
f(x)=x⁴−6x³+26x²+px+65be a_(k)+ib_(k) for k=1, 2, 3, 4.  Given that the a_(k), b_(k) are all integers, and that none of the roots are real, find p.
Original LaTeX notation
Let $p$ be an integer, and let the roots of
\[f(x) = x^4 - 6x^3 + 26x^2 + px + 65\]be $a_k + ib_k$ for $k = 1,$ $2,$ $3,$ $4.$  Given that the $a_k,$ $b_k$ are all integers, and that none of the roots are real, find $p.$

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
8b437ae0-980c-5dac-abca-8b491a9e9a8b
task_key
intermediate~5falgebra--test--8b437ae0-980c-5dac-abca-8b491a9e9a8b
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import