What's the solution of Cubic and biquadratic polynomial?

In summary, to solve equations such as ax^2 + bx + c = 0 and ax^3 + bx^2 + cx + d = 0, there are general formulas available, but they are not simple and cannot be written in a single equation. These formulas can be found on MathWorld, but it may be more efficient to use a computer program to solve these equations.
  • #1
TheDestroyer
402
1
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?
 
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  • #3
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.
 
  • #4
Thanks, Seems the best way is creating a damn program for solving this!
 
  • #5
Yes,that's the the modern method lazy people use these days...

This is far too simple maths to use a computer.

Daniel.
 

Related to What's the solution of Cubic and biquadratic polynomial?

What is a cubic polynomial?

A cubic polynomial is a polynomial function of degree 3, meaning that its highest power term is raised to the third power. It can be expressed in the form of ax^3 + bx^2 + cx + d, where a, b, c, and d are constants and x is the variable.

What is a biquadratic polynomial?

A biquadratic polynomial is a polynomial function of degree 4, meaning that its highest power term is raised to the fourth power. It can be expressed in the form of ax^4 + bx^3 + cx^2 + dx + e, where a, b, c, d, and e are constants and x is the variable.

What is the difference between a cubic and biquadratic polynomial?

The main difference between a cubic and biquadratic polynomial is the degree of the polynomial. A cubic polynomial has a degree of 3, while a biquadratic polynomial has a degree of 4. This means that a biquadratic polynomial has one more power of x than a cubic polynomial.

How do you solve a cubic polynomial?

To solve a cubic polynomial, you can use different methods such as the rational root theorem, synthetic division, or the cubic formula. The rational root theorem helps to find potential rational roots of the polynomial, synthetic division is a method for dividing polynomials, and the cubic formula gives the exact solutions of the polynomial.

How do you solve a biquadratic polynomial?

Similar to solving a cubic polynomial, you can use different methods to solve a biquadratic polynomial such as the rational root theorem, synthetic division, or the biquadratic formula. The biquadratic formula gives the exact solutions of the polynomial.

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