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Hi everyone, I was studying the cyclotomic equation and I came across an example:
x^4 + x^3 + x^2 + x +1 = 0 ; this equation cannot be factorised neither using Ruffini’s rule nor replacing an x with t. The book said that it is sufficient to divide all by x^2 and rearrange the terms to obtain –> x^2 + 1/x^2 + x + 1/x + 1 = 0, then let w be equal to x + 1/x, and the equation (I also have verified) becomes w^2 + w -1 = 0.
My question is: does it exist a formula (or a procedure) that allows to reduce an equation with a degree greater than 2 to a quadratic’ Procedures other than replace x^4 with t and x^2 with t.
In fact there would be Abel-Ruffini theorem to take into account…which says that there is not a general algebraic solution for quintic equations and higher degrees…
Could you help me please’
Accounting issue category: Financial accounting books, Managerial accounting books, Advanced accounting books.
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