In[]:=
vars={k,x,y,z,u,v,w,p};​​poly1=-2*x-4*u*v+4*y*p;​​poly2=-9*y+3*x*p;​​poly3=-4*z-4*Sqrt[2]*u*w+4*Sqrt[2]*w*p+4*k;​​poly4=-5*u+x*v+3*Sqrt[2]*z*w;​​poly5=-v+3*x*u-Sqrt[5]*x*w;​​poly6=-w+Sqrt[5]*x*v+Sqrt[2]*z*u-Sqrt[2]*z*p;​​poly7=-5*p-7*x*y-3*Sqrt[2]*z*w;​​polys={poly1,poly2,poly3,poly4,poly5,poly6,poly7}
Out[]=
-4uv-2x+4py,3px-9y,4k+4
2
pw-4
2
uw-4z,-5u+vx+3
2
wz,-v+3ux-
5
wx,-w+
5
vx-
2
pz+
2
uz,-5p-7xy-3
2
wz
In[]:=
startingPoints=Transpose[{vars,Table[0,Length[vars]]}]
Out[]=
{{k,0},{x,0},{y,0},{z,0},{u,0},{v,0},{w,0},{p,0}}
In[]:=
FindRoot[polys,startingPoints]
FindRoot
:The number of equations does not match the number of variables in FindRoot[polys,startingPoints].
Out[]=
FindRoot[polys,startingPoints]