If z be a complex number satisfying$\displaystyle\ z^{4}+z^{3}+2z^{2}+z+1=0$ then $\displaystyle\ |z|$ is 

${ z }^{ 4 }+{ z }^{ 3 }+2{ z }^{ 2 }+z+1=0$

$\left[ { z }^{ 4 }+2{ z }^{ 2 }+1 \right] +\left[ { z }^{ 3 }+z \right] =0$

$\left[ { z }^{ 2 }+1 \right] \left[ { z }^{ 2 }+1+z \right] =0$

${ z }^{ 2 }+1=0\Longrightarrow z=\pm i$

$\left| z \right| =1$

or

${ z }^{ 2 }+z+1=0$

$z=\cfrac { -1\pm \sqrt { 1-4 } }{ 2 } =\cfrac { -1\pm \sqrt { 3i } }{ 2 }$

$\left| z \right| =\sqrt { \cfrac { 1 }{ 4 } +\cfrac { 3 }{ 4 } } =1$

$\therefore \boxed { \left| z \right| =1 }$