| 41. | When a cubic equation has three real roots, the formulas expressing these roots in terms of radicals involve complex numbers.
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| 42. | He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations.
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| 43. | I did try to construct cubic equations using nested radicals of real numbers only, but always ended up with irrational coefficients.
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| 44. | The nested radicals in this solution cannot in general be simplified unless the cubic equation has at least one rational solution.
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| 45. | The remaining three roots can be obtained by using synthetic division to divide the two roots out, producing a cubic equation.
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| 46. | Around 1540, under a promise of strict secrecy, Tartaglia revealed how he had solved a famous problem called the cubic equation.
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| 47. | He understood the importance of the discriminant of the cubic equation to find algebraic solutions to certain types of cubic equations.
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| 48. | A cubic equation with real coefficients can be solved geometrically using angle trisector if and only if it has three real roots.
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| 49. | It is said that the treatise contains formulas for the volume of the sphere, cubic equations and the accurate value of pi.
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| 50. | It was Rafael Bombelli who managed to understand how to work with complex numbers in order to solve all forms of cubic equation.
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