Editing RootsOfPolynomials
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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