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!!!
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
+163 
