Find 'a'

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!!!