Question
Common roots of the equations $z^{3}+2 z^{2}+2 z+1=0$ and $z^{1985}+z^{100}+1=0$ are(a) $1, \omega, \omega^{2}$,(b) $-\omega,-\omega^{2}$(c) $\omega, \omega^{2}$(d) $-\omega, \omega^{2}$
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Step 1: We are given two equations: \[z^{3}+2 z^{2}+2 z+1=0 \tag{1}\] and \[z^{1985}+z^{100}+1=0 \tag{2}\] Show more…
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Common roots of the equations $z^{3}+2 z^{2}+2 z+1=0$ and $z^{1985}+z^{100}+1=0$ are (A) $\omega, \omega^{2}$ (B) $1, \omega, \omega^{2}$ (C) $-1, \omega, \omega^{2}$ (D) $-\omega,-\omega^{2}$
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