how do you use lagrangian resolvents to help solve polynomial equations?

[Al-Layth]

There's this brilliant.org on lagrange resolvents, and it uses it on the general cubic polynomial. it produces a quadratic equation instead.

i've tried googling more but it seems very difficult to find anything on this, and the stuff i do find is nigh incomprehensible.
i have essentially 2 questions?

1.) how do you derive the lagrange resolvent equation for a given polynomial?

2.) Can this be done to quintic polynomials?? If the purpose of this technique is to reduce the order of the polynomial to be solved then it should work on quintics too right?

 

[khansaheb]

Please define for us :- "the Lagrange resolvent equation for a given polynomial"

Now from the given information in the problem, set up the equation.

Please show us what you have tried. Did you check:

Solving Cubic Equations with Lagrange Resolvent?

I'm having difficulties understanding my textbook's decription of solving cubic equations using Lagrange Resolvents and symmetric polynomials. Here's what I understand: $$ x^3 + px - q = (x-r)(x-s)...

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