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MATH / For some real numbers a and b, the equation 8x³+4ax²+2bx+a=0has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of a?

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problem

For some real numbers aa and bb, the equation 8x3+4ax2+2bx+a=0 8x^3 + 4ax^2 + 2bx + a = 0 has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of aa?
Plain-text mathematical notation (without MathML)
For some real numbers a and b, the equation 8x³+4ax²+2bx+a=0has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of a?
Original LaTeX notation
For some real numbers $a$ and $b$, the equation \[
8x^3 + 4ax^2 + 2bx + a = 0
\]has three distinct positive roots. If the sum of the base-2 logarithms of the roots is 5, what is the value of $a$?

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
48e0741c-0154-523a-be92-d25064662fc2
task_key
intermediate~5falgebra--test--48e0741c-0154-523a-be92-d25064662fc2
task_revision_id
1
config / split
intermediate_algebra / test

Official source

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