What's the solution of Cubic and biquadratic polynomial?

  • Context: Undergrad 
  • Thread starter Thread starter TheDestroyer
  • Start date Start date
  • Tags Tags
    Cubic Polynomial
Click For Summary
SUMMARY

The discussion focuses on solving cubic and biquadratic (quartic) polynomial equations, specifically the forms ax^3 + bx^2 + cx + d = 0 and ax^4 + bx^3 + cx^2 + dx + e = 0. While there are general formulas for these equations, they are complex and cannot be expressed as simple equations. Resources such as MathWorld provide detailed formulas for cubic and biquadratic equations. The conversation suggests that programming solutions may be the most efficient method for solving these types of equations in modern contexts.

PREREQUISITES
  • Understanding of polynomial equations
  • Familiarity with the quadratic formula
  • Basic knowledge of algebraic terminology (cubic, quartic, biquadratic)
  • Programming skills for implementing numerical solutions
NEXT STEPS
  • Research the cubic formula on MathWorld
  • Explore the quartic equation solutions on MathWorld
  • Learn how to implement polynomial solvers in Python
  • Study numerical methods for solving higher-degree polynomials
USEFUL FOR

Mathematicians, students studying algebra, software developers creating mathematical applications, and anyone interested in solving polynomial equations efficiently.

TheDestroyer
Messages
401
Reaction score
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?
 
Mathematics news on Phys.org
Terminology:A biquadratic (algebraic) equation is a particular case of a quartic...E.g.
ax^{4}+bx^{2}+c=0

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.
 

Similar threads

MHB Prove No Integers Solve $ax^3+bx^2+cx+d=1$ for x=19,2 for x=62
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Quadratic, cubic, quartic, quintic equations
  • · Replies 16 ·
Replies
16
Views
5K
MHB Polynomial Challenge: Show Real Roots >1 Exist
  • · Replies 1 ·
Replies
1
Views
1K
MHB Evaluate the constant in polynomial function
  • · Replies 7 ·
Replies
7
Views
1K
MHB Understanding Cubic Equation Formula for Polynomials of Degree Three
  • · Replies 9 ·
Replies
9
Views
3K
MHB Finding Min Value of $\dfrac{|b|+|c|}{a}$ from Roots of Cubic Equations
  • · Replies 4 ·
Replies
4
Views
1K
High School Are Inverse Problems More Complex Than Direct Problems in Mathematics?
  • · Replies 13 ·
Replies
13
Views
3K
MHB Roots of a Polynomial Function A²+B²+18C>0
  • · Replies 4 ·
Replies
4
Views
1K
MHB Find (x₁²+1)(x₂²+1)(x₃²+1)(x₄²+1)
  • · Replies 2 ·
Replies
2
Views
1K
High School Understanding the relationship between ratios and fractions
  • · Replies 8 ·
Replies
8
Views
2K