Task 784
Task 784: development task in emrekuruu/math-openenv, an RL environment on the Hugging Face Hub. Find all values of the real number $a$ so that the four complex roots of \ z^4 - 6z^3 + 11az^2 - 3(2a^2 + 3a - 3) z + 1 = 0\ form the vertices of a parallelogram in the complex plane. Enter all the…
The task
Find all values of the real number $a$ so that the four complex roots of \[z^4 - 6z^3 + 11az^2 - 3(2a^2 + 3a - 3) z + 1 = 0\]form the vertices of a parallelogram in the complex plane. Enter all the values, separated by commas.