Question

If one root of the equation x⁴+x²+1=0 is α the others are -α and ±α².(Show)

*************Don't Spam"""""""""""""

Answer 1

let
${x}^{2} = t \\ eqn \: becomes \\ 1 + t + {t}^{2} = 0 \\ apply \: quad \: formula \: \\ although \: it \: will \: give \: cube \: root \: of \: unity \: but \: still \\ t = \frac{ - 1( + - ) \sqrt{1 - 4} }{2} \\ t = ( \frac{ - 1}{2} ) + ( \frac{ \sqrt{3} }{2} ) \\ ad \: \\ t = ( \frac{ -1 }{2} ) - ( \frac{ \sqrt{3} }{2} )$
check these are cube roots of unity
also the given eqn is satisfied by
cube roots of unity