What's the solution of Cubic and biquadratic polynomial?

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    Cubic Polynomial
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Discussion Overview

The discussion centers on solving cubic and biquadratic (quartic) polynomial equations, exploring the existence of general formulas for their solutions and the complexity involved in deriving them. Participants also touch on the practicality of using computational methods for solving these equations.

Discussion Character

  • Technical explanation, Debate/contested, Conceptual clarification

Main Points Raised

  • One participant presents the quadratic formula for solving quadratic equations and inquires about general solutions for cubic and biquadratic equations.
  • Another participant acknowledges the existence of general formulas for cubic and quartic equations but notes their complexity and inability to be expressed in a simple form.
  • A participant clarifies the terminology, explaining that a biquadratic equation is a specific case of a quartic equation.
  • One participant suggests that creating a program to solve these equations might be the best approach.
  • Another participant comments on the simplicity of the mathematics involved, implying that using a computer for such problems is unnecessary.

Areas of Agreement / Disagreement

Participants express differing views on the necessity of computational methods for solving cubic and biquadratic equations, with some advocating for programming solutions while others believe manual methods are sufficient.

Contextual Notes

There is an acknowledgment of the complexity of general formulas for cubic and quartic equations, but no specific mathematical steps or assumptions are resolved in the discussion.

TheDestroyer
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It's very easy to solve the equation for x:

ax^2 + bx + c = 0

The law for the answer will be (-b+-sqrt(delta))/2a

OK, what if i want to solve:

ax^3 + bx^2 + cx + d = 0
ax^4 + bx^3 + cx^2 + dx + e = 0

a,b,c,d,e constants, How I'm going to solve this for x? isn't there a general law?
 
Mathematics news on Phys.org
Terminology:A biquadratic (algebraic) equation is a particular case of a quartic...E.g.
[tex]ax^{4}+bx^{2}+c=0[/tex]

is the general form of a biquadratic equation.Do you see why it bears that name ?

Daniel.
 
Thanks, Seems the best way is creating a damn program for solving this!
 
Yes,that's the the modern method lazy people use these days...

This is far too simple maths to use a computer.

Daniel.
 

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