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0
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avatar+146 

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.

 

Thank you for helping me! All help is appreciated!!!

 Aug 15, 2020
 #2
avatar+111626 
+2

y=x^6 + 3ax^5 + (3a^2 + 3) x^4 + (a^3 + 6a) x^3 + (3a^2 + 3) x^2 + 3ax + 1

 

 

Looks like about 1.77.

 

https://www.desmos.com/calculator/gvxtwzesob

 Aug 16, 2020

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