Search for the multiple roots of the equation: x^6 + 6x^5 + 9x^4 + 36x^3 + 27x^2 + 54x + 27 = 0

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Search for the multiple roots of the equation: x^6 + 6x^5 + 9x^4 + 36x^3 + 27x^2 + 54x + 27 = 0

This question was asked by someone else and the solution was based on the function's graph. There are two roots: x=−5.449 and x=−0.551.

But I want to solve this problem by using the Rational root theorem.
I could't find any rational roots in the set p/q={+-1,+-3,+-9,+-27}.

I don't know how to proceed to find the roots.

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