cubic equation in a sentence

Examples

1. When a cubic equation has three real roots, the formulas expressing these roots in terms of radicals involve complex numbers.
2. He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations.
3. I did try to construct cubic equations using nested radicals of real numbers only, but always ended up with irrational coefficients.
4. The nested radicals in this solution cannot in general be simplified unless the cubic equation has at least one rational solution.
5. The remaining three roots can be obtained by using synthetic division to divide the two roots out, producing a cubic equation.
6. Around 1540, under a promise of strict secrecy, Tartaglia revealed how he had solved a famous problem called the cubic equation.
7. He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations.
8. A cubic equation with real coefficients can be solved geometrically using angle trisector if and only if it has three real roots.
9. It is said that the treatise contains formulas for the volume of the sphere, cubic equations and the accurate value of pi.
10. It was Rafael Bombelli who managed to understand how to work with complex numbers in order to solve all forms of cubic equation.