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MATH / Find the smallest positive real number a so that the polynomial

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Find the smallest positive real number aa so that the polynomial x6+3ax5+(3a2+3)x4+(a3+6a)x3+(3a2+3)x2+3ax+1=0x^6 + 3ax^5 + (3a^2 + 3) x^4 + (a^3 + 6a) x^3 + (3a^2 + 3) x^2 + 3ax + 1 = 0has at least one real root.
Plain-text mathematical notation (without MathML)
Find the smallest positive real number a so that the polynomial
x⁶+3ax⁵+(3a²+3)x⁴+(a³+6a)x³+(3a²+3)x²+3ax+1=0has at least one real root.
Original LaTeX notation
Find the smallest positive real number $a$ so that the polynomial
\[x^6 + 3ax^5 + (3a^2 + 3) x^4 + (a^3 + 6a) x^3 + (3a^2 + 3) x^2 + 3ax + 1 = 0\]has at least one real root.

level

Level 4

type

Intermediate Algebra

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Source and history

task_id
28081453-0a9c-5e81-99c6-2b56d2cd8fa7
task_key
intermediate~5falgebra--test--28081453-0a9c-5e81-99c6-2b56d2cd8fa7
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import