Editing RootsOfPolynomials

You are currently browsing as guest.. To change this, fill in the following fields: Username Password Click here to reset your password	Who can read this page? The World Members Council Admin
You have been granted an edit lock on this page until Tue Jan 21 01:28:37 2025. Press to finish editing.	Who can edit this page? World editing disabled Members Council Admin

A polynomial EQN:p(x) of degree n has n roots in the complex numbers. (see fundamental theorem of algebra).

If one of these roots is EQN:{\alpha} , then EQN:p({\alpha})=0

Furthermore, if EQN:p(x)=ax^n+bx^{n-1}+cx^{n-2}+...+px+q=0 has roots EQN:{\alpha}, EQN:{\beta}, EQN:{\gamma}, EQN:{\delta}, EQN:{\epsilon},...., EQN:{\omega} then

* EQN:\sum{\alpha}=-\frac{b}{a}
* EQN:\sum{\alpha}{\beta}=\frac{c}{a}
* EQN:\sum{\alpha}{\beta}{\gamma}=-\frac{d}{a}
* EQN:\sum{\alpha}{\beta}{\gamma}{\delta}=\frac{e}{a}
** etc...
** 
** 
* EQN:{\alpha}{\beta}{\gamma}{\delta}{\epsilon}...{\omega}=\pm\frac{q}{a}
*** If n is even then EQN:{\alpha}{\beta}{\gamma}{\delta}{\epsilon}...{\omega}=\frac{q}{a}
*** If n is odd then EQN:{\alpha}{\beta}{\gamma}{\delta}{\epsilon}...{\omega}=-\frac{q}{a}
----
Moreover, if one of the roots of EQN:p(x)=0 is EQN:z , where EQN:z is complex (i.e. EQN:z=x+iy and EQN:y is non-zero) and all the coefficients EQN:a,b,c...q are real then another root is the complex conjugate of EQN:z