If 
is an irreducible cubic polynomial all of whose
roots are real, then to obtain them by radicals, you must take roots of nonreal numbers
at some point.
Casus Irreducibilis
See also
Algebraic Integer, Cubic Equation, Cubic PolynomialExplore with Wolfram|Alpha
References
Dummit, D. S. and Foote, R. M. "Solvable and Radical Extensions: Insolvability of the Quintic." §14.7 in Abstract Algebra, 3rd ed. Hoboken, NJ: Wiley, pp. 625-639, 2004.Referenced on Wolfram|Alpha
Casus IrreducibilisCite this as:
Weisstein, Eric W. "Casus Irreducibilis." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/CasusIrreducibilis.html