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swampwiz
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It seems that Abel's theorem says that the quintic cannot be solved by arithmetic & root operations, but couldn't there be the situation where another function is used in concert with these operations?
swampwiz said:It seems that Abel's theorem says that the quintic cannot be solved by arithmetic & root operations, but couldn't there be the situation where another function is used in concert with these operations?
swampwiz said:It seems that Abel's theorem says that the quintic cannot be solved by arithmetic & root operations, but couldn't there be the situation where another function is used in concert with these operations?
A quintic equation is a polynomial equation of the fifth degree, meaning it has a highest degree of 5. It can be written in the form ax^5 + bx^4 + cx^3 + dx^2 + ex + f = 0, where a, b, c, d, e, and f are constants and x is the variable.
No, not all quintic equations can be solved. Some quintic equations have solutions that can be expressed using radicals, while others cannot be solved by any formula. This is known as the Abel-Ruffini theorem.
There is no general formula for solving all quintic equations. However, there are specific formulas for solving certain types of quintic equations, such as depressed quintic equations or symmetric quintic equations.
This was proven by mathematicians Paolo Ruffini and Niels Henrik Abel in the early 19th century. They showed that there is no general formula for solving quintic equations using only the four basic arithmetic operations (addition, subtraction, multiplication, and division) and taking roots.
Yes, there are other methods for solving quintic equations, such as numerical methods and approximations. These methods involve using computers or calculators to find approximate solutions to the equation. However, there is no exact formula for solving all quintic equations.