Anyone know how to solve a quintic or quartic?

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In summary, the conversation discusses the difficulty in solving quintic and quartic equations, with the possibility of using the quartic formula for quartic polynomials. It also mentions using the remainder theorem, but notes that it may not always be successful.
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13habelbrea
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Anyone know how to solve a quintic or quartic? (thanks)
(try to list your information, its helpfull!)[/CENTER]
 
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The code did not work so for get the "(/center)" in my question
 
  • #3


There is no equivalent to the quadratic formula for quintic polynomials if that's what you're getting at. There is for quartic polynomials, but it's not something you really want to use.

http://planetmath.org/encyclopedia/QuarticFormula.html

Can you explain a bit more what you want to do? Is it really just solve a general polynomial?
 
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  • #4


The easiest way would be to use the remainder theorem, but that's hit/miss. A lot of times you can use the coefficients to get the result you're after, but that depends on the application.
 
  • #5


I am familiar with the methods used to solve quintic and quartic equations. These types of equations can be solved using a combination of algebraic techniques and numerical methods such as Newton's method or the Durand-Kerner method. Additionally, there are also specialized algorithms such as the Ferrari's method for solving quartic equations and the Bring radical for solving quintic equations. It is important to note that these methods may not always provide exact solutions, but can give approximations that are accurate enough for practical purposes. It is also helpful to have a strong understanding of complex numbers and their properties when attempting to solve quintic and quartic equations.
 

FAQ: Anyone know how to solve a quintic or quartic?

What is a quintic or quartic equation?

A quintic equation is a polynomial equation of 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. A quartic equation is a polynomial equation of the form ax^4 + bx^3 + cx^2 + dx + e = 0. These equations are called quintic and quartic because they have degrees 5 and 4, respectively.

Are there specific steps to solve a quintic or quartic equation?

Yes, there are specific methods for solving quintic and quartic equations. However, these methods are complex and require advanced knowledge of algebra and mathematics. They are not commonly taught in most high school or undergraduate math courses.

Can any quintic or quartic equation be solved?

No, not all quintic and quartic equations have solutions that can be expressed using radicals (square roots, cube roots, etc.). This was proven by the mathematician Galois in the 19th century. However, there are other methods for solving these equations, such as using numerical methods or approximations.

Why are quintic and quartic equations difficult to solve?

Quintic and quartic equations are difficult to solve because they do not have a general formula for finding solutions, unlike quadratic and cubic equations. This means that each equation must be approached and solved in a unique way, using different methods and techniques.

What are some real-life applications of quintic and quartic equations?

Quintic and quartic equations are used in various fields, such as physics, engineering, and economics, to model and solve problems involving motion, growth, and optimization. They are also used in cryptography and coding theory for secure communication and data encryption.

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