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. Abstract Algebra, 1st ed. Englewood Cliffs, NJ: Prentice-Hall, pp. 547 and 551, 1998.Cite this as:
Weisstein, Eric W. "Casus Irreducibilis." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/CasusIrreducibilis.html