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MATH / Suppose that all four of the numbers 1−√(2), 3+√(7), 1+√(2), 5are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polyn…

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problem

Suppose that all four of the numbers 1−2,3+7,1+2,51-\sqrt{2}, \;3+\sqrt{7},\;1+\sqrt{2},\; 5are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?
Plain-text mathematical notation (without MathML)
Suppose that all four of the numbers 1−√(2), 3+√(7), 1+√(2), 5are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?
Original LaTeX notation
Suppose that all four of the numbers \[1-\sqrt{2}, \;3+\sqrt{7},\;1+\sqrt{2},\; 5\]are roots of the same nonzero polynomial with rational coefficients. What is the smallest possible degree of the polynomial?

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
182f1585-616f-56a4-b1a5-20e65f8845a8
task_key
intermediate~5falgebra--test--182f1585-616f-56a4-b1a5-20e65f8845a8
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import