﻿ Formulas to solve Polynomial Equations.
 Formulas to solve Polynomial Equations.

The general form of the nth degree equation is:  a0xn + a1xn-1 + a2xn-2 + ... + an-1x +  an = 0

The nth degree equations have always n roots.  In particular cases, some or all of this n roots could be equal to one another.

If the coefficients ai are real numbers, then the roots could be real or complex  numbers.  (Any combination, with the following restriction: if one of the roots is complex, then its conjugate is also a root.  This implies that complex roots comes in pairs and that odd degree equations have at least one real root.)

 First degree equations: ax + b = 0One root: Second degree equations (or Quadratics): ax2 + bx + c = 0 Two roots: and Third degree equations (or Cubics): ax3 + bx2 + cx + d = 0 Three roots: Press here to see them (the formulas are really big). Fourth degree equations (or Quartics): ax4 + bx3 + cx2 + dx + e = 0 Four roots: Press here to see them (the formulas are even bigger). Equations of degree higher than four: The roots of equations of degree higher than four can't, in general, be expressed using only the operations of addition, subtraction, multiplication, division and extraction of nth roots [Ruffini, Abel, Galois].  However, these roots can be found with numerical algorithms. First post in: 2002 Last update: 2006-02-04