x6+ax5+b=0

Simplest examples of irreducible and solvable by radicals sextic trinomials, x⁶+ax⁵+b, where a and b are integers in range [-1111..1111]. Excluded trivial cases where a or b are equal zero.

Basic notes:

- if x⁶+ax⁵+b=0 is solvable then x⁶-ax⁵+b=0 is too. More generally x⁶+ax⁵+b=0 is solvable if and only if x⁶+acx⁵+bc⁶=0 is solvable (c is non-zero rational number).

- if x⁶+ax⁵+b=0 is solvable then x⁶+(a/b)x+(1/b)=0 is too. And in more general: x⁶+(ac⁵/b)x+(c⁶/b)=0

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