technique on finding roots of a polynomial?

[striker_24]

Mga sir,meron po ba kyong idea kung pano kumuha ng roots ng isang 3rd degree (or higher) polynomial without using synthetic division?

Meron po bang technique jan?

Salamat!

striker_24

[zer0w1ng]

If by hand, factoring is another method in finding roots of a higher degree polynomial

Using computers, Newton-Raphson method can be used.
http://en.wikipedia.org/wiki/Newton's_method

But it only find a single real root one at a time.

[eveready battery]

using cardan's or cardano's cubic equations

http://www.trans4mind.com/personal_development/mathematics/polynomials/cubicAlgebra.htm

using ferrari's quartic equations

http://members.tripod.com/l_ferrari/quartic_equation.htm

[emmgon]

If you are looking for a numerical method for solving such problems, try the Method of Successive Substitutions... easily found in the Internet and the algorithm is very easy.