question_answer

Quadrilateral formed by the points corresponding to the roots of \[{{z}^{4}}-{{z}^{3}}+2{{z}^{2}}-z+1=0\] is a

A) Square               

B)                              Parallelogram which is not a square

C) Trapezium         

D) Rhombus which is not a square

Correct Answer: C

Solution :

  [c] \[{{z}^{4}}-{{z}^{3}}+2{{z}^{2}}-z+1=0\] \[\Rightarrow \,\,\,\,({{z}^{2}}+1)({{z}^{2}}-z+1)=0\] \[\Rightarrow \,\,\,\,z=\pm i,\,\,\frac{1\pm \sqrt{3}i}{2}\] From the figure, it is clear that the quadrilateral is a trapezium (ABCD).