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Omni-MATH / Determine all real values of the parameter a for which the equation

Problem

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

problem

Determine all real values of the parameter aa for which the equation 16x4−ax3+(2a+17)x2−ax+16=016x^4 -ax^3 + (2a + 17)x^2 -ax + 16 = 0 has exactly four distinct real roots that form a geometric progression.
Plain-text mathematical notation (without MathML)
Determine all real values of the parameter a for which the equation
16x⁴−ax³+(2a+17)x²−ax+16=0
has exactly four distinct real roots that form a geometric progression.
Original LaTeX notation
Determine all real values of the parameter $a$ for which the equation
\[16x^4 -ax^3 + (2a + 17)x^2 -ax + 16 = 0\]
has exactly four distinct real roots that form a geometric progression.

Discussion

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Source and history

task_id
253b3ad7-3b70-563f-a624-943dbd66ce59
task_key
test--253b3ad7-3b70-563f-a624-943dbd66ce59
task_revision_id
1
config / split
/ test

Official source

initial import