x6+ax+b=0

Simplest examples of irreducible and solvable by radicals sextic trinomials, x⁶+ax+b, where |a| and |b| are integers not bigger than (at least) 33,000,000. Excluded trivial cases where a or b are equal zero.

Basic notes:

- if x⁶+ax+b=0 is solvable then x⁶-ax+b=0 is too. More generally x⁶+ax+b=0 is solvable if and only if x⁶+ac⁵x+bc⁶=0 is solvable (c is non-zero rational number).

- if x⁶+ax+b=0 is solvable then x⁶+(a/b)x⁵+(1/b)=0 is too. And in more general: x⁶+(ac/b)x⁵+(c⁶/b)=0

Trinomials of the group 6T13 up to 36,500,000

Trinomials of the group 6T11 up to 33,700,000

See incredible explicit formulas for the roots of the solvable polynomials.