Find all values of the real number a so that the four complex roots of z4−6z3+11az2−3(2a2+3a−3)z+1=0 form the vertices of a parallelogram in the complex plane. Enter all the values, separated by commas.
a=3 is the only answer I see.
Thanks Rom but how did you find it ?
(Melody)
well....
I coded up a Mathematica sheet that plotted the 4 roots on the complex plane as I adjusted the parameter a.
Having seen it was right about 3 I then checked the roots.
Unless there's some trick this is an absurdly difficult problem w/o software.
ok thanks Rom
Thank you so much! :)
+142 
