Methods of Solving Nonstandard Problems by Ellina Grigorieva

Author:Ellina Grigorieva
Language: eng
Format: epub, pdf
Publisher: Springer International Publishing, Cham

It is interesting that the original polynomial looked like one of 6th degree, but the 6th degree terms were cancelled and we obtained three real roots and two complex roots for a polynomial function of the 5th degree by factoring and solving a symmetric quartic equation.

2.7.1 Euler’s Method for Solving a Quartic Equation

Consider the equation .

Then find its cubic resolvent as

and its roots z 1, z 2, z 3.

Then solutions to a quartic equation are

(2.99)

The roots can be complex. Note that the signs of the roots are selected by the rule

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