Question

Quadrilateral formed by the points corresponding to the roots of
$z^4-z^3+2z^2-z+1=0$ is a-

• A. square
• B. parallelogram which is not a square
• C. trapezium
• D. rhombus which is not a square

Answer 1

Answer: (C)

trapezium

$z^4-z^3+2z^2-z+1=0$
$\Rightarrow (z^2+1)(z^2-z+1)=0$
$\Rightarrow$ $z=\pm i,-\omega ,-{\omega }^2$
Hence quad ($ABCD$) is a trapezium